The above question was posted on an online message board for consumers. Read my response below.
The maximum you can invest/save into an ISA each year is £20,000 so, depending upon the amount you have inherited, it may take a number of years to move them fully into an ISA.
It also depends upon where the shares are held. If they are held on an investment platform such as Hargreaves Lansdown or Interactive Investor, you should be able to transfer them from the share dealing account to an ISA account pretty easily and at a relatively low cost.
However, if they are directly held shares through a dealing account that doesn’t provide ISA wrappers, you will need to sell sufficient shares to the value of £20,000 each year and then once you have received the proceeds re-invest them into an ISA. There will be share dealing costs for each sale every year, typically of around £15 but possibly higher and be mindful of potential CGT, though at £20,000 that is not likely with the annual CGT allowance (currently £12,300)
You might also be aware that investing in a smaller number of individual company shares is much riskier than investing across global stock markets where the effect of one or two companies performing poorly will be significantly reduced for you. Not only that, by investing across stock markets you are going to be guaranteed to hold the future winners even if you don’t which companies they are yet.
On this basis, you could sell all the shares you hold (but be aware of potential capital gains tax liability) and invest in a range of global stock market indices. This would also make it easier to use your ISA allowance each year.
Of course, the shares you currently own could do better than the main stock markets as a whole but it is a higher risk strategy.
The above does not constitute advice.