Hi,
I assume you are a US Citizen, (otherwise why would you be posting here!). If so, then you are liable to file taxes in the US regardless of how long you've spent there (even if you've never been there!).
Usually, if you're living in the UK you will not need to actually pay US taxes, either because the Foreign Earned Income Exclusion (which excludes the first $91,500 of foreign earned income) or the Foreign Tax Credit (so if you've paid taxes in the UK, you can claim it as a credit in the US). Since UK taxes are (generally) higher than the US, most people won't ever need to pay US taxes. However, if you have UK-tax-free income (such as capital gains or interest in a ISA or SIPP) then there could be a US liability (since the Foreign Earned Income exclusion only covers earned income not savings/investment income).
Another exception is SE (Self Employment tax). Technically, the FEI or the FTC won't cover the SE tax (which is the equivalent of class 4 National Insurance here). However, there is a totalization agreement between the US and UK which means that if you're covered by one social security agreement, you don't need to pay for the other. Hence the need for the US/UK 1. More details here:
http://www.ssa.gov/international/Agreement_Pamphlets/uk.htmlEven though you may, due to the above, have no US tax liability, you are still required to file if you earned (if single) around $9350 (£5700).
However, if you are self employed, you'll need to file if you made at least $400 (£245), so you will probably need to file, with schedule C.
The good news is that you may be entitled to a refund (due to Making Work Pay etc).
In addition to all this, if you have or had $10,000 in a bank account outside the US at any stage, you'll need to file an FBAR (Foreign Bank Account Report).
Let me know if you need any more information, and good luck with the band
All the best
Andrew