I did this a few years ago. Worked with the solicitor who was the executor and they 'assented' the house out of the estate, so effectively transferred it into the names of all the beneficiaries before probate was granted, as opposed to selling it to then putting the money into the estate and distributing it. We were all happy with this, (including the executor,) and had agreed that it would be sold to the beneficiary that wanted to buy the rest out.
That meant that the transaction around selling the house was separate from probate and the executor could get on with the rest of the process. The value of the house was still included in the value of the estate for probate purposes, even though it had been effectively 'distributed' to the beneficiaries.
We than had an independent surveyor (not an estate agent) come and do a full survey, including valuation and indicator of what work needed doing which meant we could get some quotes / ideas of what the market value was. So, say it was worth £250k but had £20k worth of work to do, the market value was £230k and that was the price agreed for the sale between beneficiaries.
We then used the same solicitors firm, but their conveyancing department, to do the necessary work around the sale and conveyancing of the property. The beneficiary who wanted to buy it had a mortgage lined up already and it was a very simple and quick process. We didn't do searches or any of the other stuff that slows a sale as the beneficiary buying it already owned part of it, so no requirement from the mortgage company to do them. They classed it as a remortgage and used the proportion held by the buying beneficiary as the deposit.
We all had the one solicitor for the conveyancing, (I checked with another legal firm who confirmed it was not a conflict of interest,) and agreed amongst ourselves the proportion of the cost of the conveyancing we would pay, so the buyer paid e.g. 50% of the overall cost as the 'buyer' and then 25% of the remaining 50% as there were 4 beneficiaries who were the 'seller'.
As it was all agreed and amicable and the will was clear and uncomplicated (and written by the same firm of solicitors who executed it,) there were no issues, it was quick, much quicker than an ordinary sale and could have been quicker if we'd wanted the conveyancing solicitor to do it faster. We just wanted some time to clear the house properly before the sale and so it could be moved into as soon as the sale was finalised.
The mortgage company transferred the funds to the conveyancing solicitor and they transferred the proportion owed to each remaining beneficiary straight away - took about 30 minutes!
All together it took a few weeks, the only delay, which had no impact on the sale or the new owner moving in, was getting the documents back from the Land Registry which took several months; which is pretty normal. We got the assent documents first and then a month or so later the full transfer of ownership to the beneficiary that bought it.