You could move the shares into a stocks and shares ISA although you would need to make a disposal in order to do so - i.e. sell them and buy them back within the ISA. This could trigger a capital gain which you may have to pay capital gainstax on, or if as you say, they are worth less than when you inherited them you could crystallise a capital loss which can be carried forward indefinitely to offset against future gains.
To ensure you do not oversubscribe for your ISA you could sell shares up to your allowance this tax year and then some more in the new tax year to fund the new allowance. Once the shares are within the ISA any gains will be free of capital gains tax - so it would be prudent from a tax perspective. Also if you are not going to utilise your ISA allowance any other way it means you make use of the annual allowance which otherwise would be lost.
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