Has probate been granted though?
If not, then the property is now the property of the estate and the cash proceeds from the sale of the house will replace the estimated value they have currently included in the probate calculations (and a refund for any IHT then overpaid can be reclaimed)
No CGT should be payable assuming it was her principal place of residence.
If, however, probate has been granted, although you say the property is in her name still, the property would be owned by the beneficiary of the will that inherited it. That said, no CGT should be payable if it sells for less than probate value. You might, however, want to see if the probate value can be amended anyway, so as to reduce any IHT that is payable.
There is a warning in the IHT/CGT manuals that some unscrupulous people might have overstated the property value for IHT purposes, especially where no IHT is payable, then sold the property later for a "loss", to avoid CGT and create a capital loss that they can carry forward against future gains. Make sure you have evidence of the property valuations at the point of probate if it remains unchanged for IHT purposes.
Beware that a CGT return might need to be submitted to HMRC within 60 days of any sale, whether there is CGT to pay or not. The conveyancing solicitor should assist with this.
I would recommend, if you aren't already, getting a probate specialist solicitor involved in handling the probate.