Arthur Weller replies:
In essence, what you are claiming is that although the house was entirely in your mother's name, she was the 100% legal owner, nevertheless you owned (at least) 20% of the beneficial ownership of the property, by virtue of the fact that you paid for it, and jointly occupied the property together with your mother. If you look at www.gov.uk/hmrc-internal-manuals/capital-gains-manual/cg70230 you can see that according to the criteria listed there you have a good argument. I would advise you to do as you have written (deduct the £80,000), but explain to HMRC what you are doing (quoting CG70230) so that they cannot question you later.
This question was first printed in Property Tax Insider in April 2017.