Hi Neil,
Investing in an ISA won't mitigate an already existing Capital Gains Tax (CGT) liability. It will mean that you won't accrue any new CGT once the money is in an ISA.
You could look at an EIS (Enterprise Initiative Scheme). This won't reomve the CGT liability immediately bu tit will defer it. Furthermore, you will get 30% income tax relief, which will be helpful as you have stated you are a higher rate taxpayer.
You will need to speak to a financial adviser as this area is slightly complicated. You will need to keep the EIS for at least 3 years in order to get the CGT deferral. You can then take the cash out from the EIS, retain the £10,000 (ish) Capital Gains Tax Allowance and re-invest the balance into a new EIS and get another slug of 30% tax relief.
Check out companies such as Octopus or Stellar Asset Managment and have a look at their information to help decide whether this may be of interest to you.
Hope this helps.