Hi Molly
To cut a long story short, I had expected to leave the country a few years ago, so decided to file a tax return to claim overpaid tax.
They said I had to file all the tax returns for the 4 tax years I had been here in order to claim overpaid tax for the first of those 4 years I was here. But it was fine with them that I had to go back that far, and I even went into an Inland Revenue (as it was known then) office in central London and got to talk to a real live tax advisor after having gotten as far as I felt I could do by phone calls.
Long story short, I successfully filed the returns for all the years I had been here, and was paid a whopping £1000 in overpaid tax (I say whopping because it was only a case of having become a UK taxpayer in June of my first year, two months after the start of the tax year - all years since then I had been paying the right amount of tax).
My advice is to call the HMRC helpline and enlist their support, and follow through with it all, you could end up reclaiming lots of overpaid tax, making your efforts very well worthwhile!