Can losses from shares be offset against tax

In almost every case what Aark says is spot on. There are exceptions but only in respect of certain types of shares.

Broadly speaking, if the shares were acquired by subscription (not by gift or purchase) and the company was an unquoted trading company (including AIM) then any subsequent capital loss can be set against your income tax liability.

To claim such an allowable loss you need to complete the CGT pages of the SA Return.

If you "subscribed" for the shares in question there may also be income tax relief via that route.

Any losses made on the disposal of qualifying EIS shares can be offset against any gains made which are subject to CGT and, in some cases, income tax.

CVS [Corporate Venturing Scheme], unlike EIS relief for individuals, does not give capital gains tax exemption on disposal. On a disposal at a loss the capital loss (net of the 20% investment relief) may be offset against income tax.

If they were "non-AIM" shares which you bought perhaps via a broker from the UK market it looks like you are restricted to utilising your Loss against future Capital Gains only, as Aark says.

Don't forget that a Capital Loss is not allowable until it calculated and notified to HMRC. There is a time limit of 5 years 10 months from the tax year in which it arose.