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If you have made a profit on the shares you have bought and sold (a "capital gain" )you will have to pay capital gains tax (CGT) at the rate of 18%. CGT is assessed on the aggregate net gain of the appropriate tax year, so those shares you have sold at a loss will be taken in to account.
CGT is payable on or before 31st January following the end of the of the tax year in which the gain occurred. If you only started dealing in shares in May 2009 then this is included in the tax year 09/10 (ie. from 06/04/09-05/04/2010) and is therefore payable by 31st January 2011. As long as you get your assessment return in (with the tax payable) in good time before then you will be fine.
You can complete it online yourself if you register of online-self assessment, HMRC's site is pretty good and user-friendly: http://www.hmrc.gov.uk/cgt/index.htm
There are various reliefs which you may be able to take advantage and if you share dealing history is complicated (or you derive income from a number of different sources (eg. from businesses you have an interest in, employment, savings) you may consider instructing an accountant to prepare your tax return.
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