Lily cops a lot of stick, doesn't she? A lot of people really don't like her. Especially rock hacks, I gather. It's that lingering suspicion that someone tainted with a 'celebrity' profile has no place in our orbit. And the nepotism charges. And the fact that she's a bit mouthy. Shame really, because what comes out of said mouth is often a breath of fresh air.

Allen's is an off-the-cuff feminism that doesn't reconcile career consequence when she's got a handle to fly off. The occasional foot in mouth moment seems a reasonable trade-off for having someone who grasps issues about representation and hypocrisy with specificity rather than settles for vacuous, please-everyone homily. Way ahead of release, she's already duking it out over the contents of her second album. There's been a minor squall over the opening cut 'Everyone's At It' ("when will we tire of putting shit up our noses"). Either she's a genius at self-promotion – and I don't think she is – or, as is her wont, this is just another in a long line of highly literal, unadorned lyrics ("I get involved, but I'm not advocating").

Sometimes she's not getting enough juice out of her backing tracks (more Pet Shop Boys-ey this time around) but Allen is certainly growing both as a singer and lyricist. She's developed a distinctive, easy vocal presence that channels her 'take me as I am' open-handedness perfectly. She can labour a rhyme, it's true, but there are always compensatory moments of eloquence. And anyone who can conjoin "suicidal" with "Credence Clearwater Revival" ('Him') is OK in my book. An unflinching, grounded storyteller, Allen conjures up a world in which other girls are taller and prettier, but a Chinese takeaway and a cup of tea can soothe most of life's problems (if not, there's always the credit card). She's not yet as sure-footed on 'bigger' issues; her put-down of bigotry on 'Fuck You', to the backing of what sounds like Mary Poppins' chorus line, seems just a little bit too worthy.

Allen is best when she shoots from the hip; I wouldn't want to be outed as the boy with impeccable manners but bedroom performance issues in 'Not Fair'. Elsewhere she's harder on no-one more than herself, and she'd be a lesser writer if she ever attempted to mask the biting insecurities that serve as the energetic to many of her best songs. For all the talk of maturity and 'difficult second album' syndrome, Allen still sounds youthful. There's also a good eye for detail that would doubtless be better recognised were she a male writer. Nowhere more so than on birth of a relationship saga 'Who'd Have Known' - a romantic tryst with added commitment anxiety perfectly encapsulated as having "just the right amount of awkward".

She closes out with 'He Wasn't There', about father Keith. Despite the accusatory title, it's ultimately placatory – a generous three parts adoration to one castigation. Fascinating how the song normalises her old man back into the traditional father-daughter narrative that she's claimed she craved as a child ("I'll always be your little girl", she asserts, as if glueing together her heart's broken crockery). There's a lovely reference to "his ex-wife" - Lily's mother, of course - that is perfectly once removed from the doubtless messy realities. It's just one further demonstration of her growing stature as a writer and diarist.