pedalhead – not sure the advice you got was correct. The actual value of the property for mortgage purposes will still be £450K or so, in which case the property cannot be undersold without the risk of stamp duty being retrospectively levied on the real value rather than the free transfer.
Edit – there’s **potentially** (hard to say based on the info above) also an issue of beneficial interest if person A continues to live in the property – strictly speaking that could make person B subject to capital gains unless they live there before the property is sold on or disposed off via probate, and even if no rent is paid HMRC may decide that it’s effectively an informal rental arrangement with reservation of future benefit issues.
Quite a complex scenario and I’ll be watching the subsequent replies from more knowledgeable folk with interest.