Photograph courtesy of Kate Bones

South Queensferry is a picturesque old town on the banks of the Firth of Forth. Stationed between the river's iconic road and railway bridges, it's a realm of blurred and eddying boundaries – between city, countryside and coast; land and sea; history and industry. Before the bridges existed, it was a ferry crossing from Edinburgh to Fife, and since then it's thrived on making connections – ancient, modern, geographical, social – and composer/pop alchemist Anna Meredith grew up there.

Meredith, now based in London, has written music for Hong Kong park benches, Singapore sleep-pods, M6 service stations and Suffolk MRI scanners. She's shared bills with Anna Calvi, James Blake and These New Puritans, versed Goldie in the world of classics, written concertos for human beatboxers and was composer in residence for the BBC Scottish Symphony Orchestra. Her recent BBC Proms performances have spanned a body-percussion magnum opus, collaborations with Laura Marling and The Stranglers (for the debut 6 Music Prom), and a composition for the last night of the Proms, 'Froms', which was simultaneously played by five symphony orchestras across the UK and broadcast to 40 million people.

Caught your breath? Her thrilling debut album, Varmints was released last month on Moshi Moshi.

South Queensferry's one of those places that isn't one thing or another – it's not in the city, nor quite in the country; it's defined by bridges to other people and places – and I wondered if that landscape is reflected in the sociable, accessible, boundary-crossing music you make?

Anna Meredith: Yeah, it's a slightly strange place to grow up, South Queensferry – in that your postcode's Edinburgh, I went to school in Edinburgh, most of my mates lived in central Edinburgh, and I went to orchestras and music groups every night there after school – but I spent most of my teenage years wishing we actually lived in the city. I feel like I spent half my life back then on incredibly infrequent buses. There was this amazing bus that used to go back and forth late from the city centre, it was called the Night Reveller – isn't that a great name for a bus? You had this kind of Sophie's choice between either a bus at quarter past midnight and then there was nothing till quarter to three. So you'd just be sat there, on Waverley Bridge, in your tiny little sparkly dress, waiting and waiting for the Night Reveller. Or the Night Hawk, that was another one. They were always like the seventh circle of hell, those buses, with everyone being sick, winding through all the little rural villages out of the city…

As much as those nocturnal odysseys sound faintly gothic and grim (and familiar), they also underscore ideas of human contact, and progression, which seem to be at the heart of your work – from your Connect It symphony, which embraced the human body as instrument and orchestra, to Varmints: an album of driving, communal party music.

AM: Composing can be really isolated. You write the piece, you hand it over to an orchestra, and that's the end of your relationship. You're not involved with the performance at all. But I guess I've always had this nagging idea that I wanted to be doing stuff with people – that's why me and some friends put together the Camberwell Composers' Collective. I'm quite a people person, so it feels pretty weird that I've ended up mainly doing this thing where I'm on my own for days and days and days on end, just sitting in my pants and hoodie, thinking, "Oh god, I really need to see somebody soon." That's why playing in a band, with this record, is so much fun.

How did making the album compare to your classical commissions, in terms of how you decided on instrumentation – especially with regard to what traditional or synthesised sounds you used? There's everything on there from cello, clarinet and xylophone, to all manner of bombastic and sublime electro divinations…

AM: Everything comes from a really practical place – it's not like there's been a guiding artistic principle that's governed it all. I'm not a craftsman, I'm not somebody who enjoys spending hours finding a vintage synth, or a valve, or whatever. If it can work with really shitty sounds, then I'm happy, because that means the material's good. But I've also got a brilliant band, so we work with whatever sounds best.

You sing on Varmints – that's a new progression…

AM: Yeah, singing was a bit scary, and it's definitely a step on from anything I've ever done before. But there's a real accountability thing with this album. I wanted it to tie in with it feeling like I've done everything on it, and I also always want to push myself. I can't think of anything – in a musical sense – where I've ever said: "Oh no, that's too much for me." Or, "I can't do that, it's too scary." So even though I definitely do not have the best voice, it is my voice, and that's what this whole thing is about. It's honest. It's not very polished. But that's how I sing – like a squeaky five-year-old boy [laughs]. I've made that work for me. I've got loads of amazing singer mates that I could have used, but I wanted not to make it seem like anyone else. I really wanted to make it clear that there was no one else behind the record. There's not some dude behind the scenes who's actually doing all the stuff. This has, from start to finish, been my thing.

And when I've done everything, start to finish, I think it's important to point that out. Hopefully it's also a good role model for younger girls, to feel that they can do it. Whenever I'm teaching teenage girl composers, the one thing I always say is don't be too daunted by stuff you don't know how to do. Because, having dipped my toe into this whole world, I've realised that there are as many factions and preconceptions and problems and rules [in pop] as there are in classical music. Someone, somewhere will always tell you what they think you should be doing. But all you should really be doing is working out what you want to do, and what you can do for yourself.

You also explore your lyrical voice and language on Varmints. Even the titles seem loaded with poetry or incongruity, from 'Taken's galloping choral euphoria, which feels like it gives us everything (and then some), to the woozy, wordless diction of 'Honeyed Words'.

AM: I've been thinking of titles in some form for years, but it's been interesting watching how they evolve. I like the idea that something's not quite what you think it's going to be. And quite a lot of the album track titles are slightly – I dread to use the word steam-punk – but it's that idea of something being archaic but powerful, or spindly but massive, in whatever form.

There's a glorious cognitive dissonance in tracks like 'Nautilus', whose title evokes a fairly fragile mollusc, but whose sound is colossal and brawny and blazing with rock-opera histrionics.

AM: Exactly – and that's gone on in lots of my classical stuff as well. Like 'Axeman for Electric Bassoon', where you look at a bassoon player, but it's wired up to an electric guitar pedal, so again it's that idea that what you see, or what you expect, is not what you hear.

Other titles are founded on mythology and memory. I'm sure I once read that your early EPs – Black Prince Fury from 2012 and Jet Black Raider, 2013 – were named after your mother's imaginary horses.

AM: [laughs] That's right – isn't that brilliant? My mum and her friend, when they were about eight, they thought they were imaginary horses. I've known about it forever, because whenever her friend would call, she'd be like, "Oh, that's such-and-such – she's the one from the days when we used to think we were horses." So I've always had those names in my head. And now they're records.

I love that idea of taking something abstract or imagined and making it physical; of creating a monument to a reverie. There are these giant horse-head sculptures near us, The Kelpies, and every time we pass them, my daughter's fascinated by the fact that they're what she calls "myths made out of metal"...

AM: Yeah, I love that too. It's like taking a bit of something and making it whole. I guess that's a lovely thing about doing this album – and it's opposed to everything else I've done in my life – which is that it actually exists. First of all, and I know every band in the world must have this problem, but, as a composer, it seems amazing to put so much time and energy into something that nobody's even asked for. That's a very strange idea to me. Normally, with commissions, people are paying me, and there's a deadline, and there's a structure. But with stuff like this, with making an album, you're living on the belief of the future of the whole thing.

And now these EPs, this album, are things. They're objects. Whereas anything else I've written is played once and then possibly never played again. All that weird process of building and creating something that's just a moment in time and then passes on forever is quite a strange thing to get your head around. So it's lovely to actually make something physical, that you build out of nothing.

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They're building a new Forth bridge in South Queensferry later this summer. It promises an original, improved and uncharted mode of forging connections, defying limitations and bringing people and places together. It's an inspired idea, but not unprecedented. Some of its restless natives have been breaking that very ground for years.

Varmints is out now on Moshi Moshi. Anna Meredith plays Glasgow Hug and Pint on May 17 before touring, including a set at Field Day on June 11; for full details and tickets, head here