You've omitted some very important information. i.e. you've not told us about your earnings from April 2007 (the start of the tax year) and August 2007.
If you were employed, and paying PAYE, the tax you paid on your earnings would have been calculated on the assumption that you'd continue to earn at the same rate throughout the year. Because your income has since dropped, you might have a fairly small amount of over-paid tax due to you.
If you were to you come off JSA completely , you'd automatically be issued with a new P45, which would show your total income for the tax year (i.e. your gross pay from April to August plus the total JSA paid to you). It would also show how much tax you've paid so far in this tax year. Your new employer would automatically adjust your tax and you'd be refunded any excess tax through your pay.
As you'll still technically be on JSA, you might not automatically get a P45. You should ask the staff at JobCentre Plus to ensure that you're provided with a document showing your total income and tax paid, for the current financial year, prior to the date that you commence work. Once your new employer has that document, they should be able to adjust your tax accordingly (including paying you any tax refund due to you).
Chris