Just for clarification, say your UK income from 6 April 2009 to 5 April 2010 is £50,000:
The first £6,475 is tax free.
The next £37,400 is taxed at 20% (£6,475 tax free + £37,400 at 20% = £43,875).
The next £6,125 (£50,000 - £43,875) is taxed at 40%.
So your taxes would be:
£37,400 at 20% = £7,480
+£6,125 at 40% = £2,450
or a total of £9,930 tax due.
Don't forget any interest you may have received from a UK bank or building society account. If you received £5, HMRC will want tax on it. In the above example, the tax on the £5 would be at 40%. If your total income (wages + interest) was below £43,875, but above £6,475, it would be taxed at 20%.
And don't be afraid to call HMRC if you have any questions. They're quite helpful.
I am not a tax professional, only a punter, so if I'm wrong about any of this hopefully the qualified people on this site can correct me.