Note the probate value doesn't determine how much tax the estate pays in the end - it determines how much must be paid up front to HMRC in order to be given probate in the first place. The final IHT reckoning obviously looks at actual sale price rather than probate value. Most estates have very little cash and so valuers know their clients expect as low a value as they can get away with to minimise any upfront cash demands from the revenue.

A probate value of £X also doesn't absolve the executors of their duty to get the best reasonable amount for the asset; if the probate value is £100k and a later estate agent advises to market at £120k and take offers of £110k, they would be failing in their executor duty to continue to rely on the original probate valuation - and open themselves to litigation by the beneficiaries.

Would also echo that money and family are a generally terrible combination. At least one party will always feel done over and resentment lingers, in my experience!

To add a bit more to my story, the Will actually specified that two valuations be done. They came back with very different figures ie £375k and £300K there was then a deduction made because the house had an agricultural occupancy condition imposed when it was built which knocks 25-30% off. It was very important that the beneficiaries were involved in agreeing a sale price and understood exactly how a final price was arrived at.
Luckily the family is very close and didn't fall out but in a lot of families this would have been a nightmare.

note to self Never ever be an Executor, you are liable for all sorts of things not only from the beneficiaries who can sue you if they think you have short changed them but also HMRC to whom you are personally responsible even for unpaid tax years before. A solicitor will have liability insurance but you won't.