I assume that the deceased estate does not have enough liquid cash to pay the Inheritance Tax liability. Normally, in such a situation, the estate's assets are sold to provide the cash to pay the tax with the balance of the cash going to those named in the will as the legatees. The property would not normally be put into the name of the person it was left to before the IHT liability was settled unless some kind of guarantee was in place.
If the probate value is £250,000 and the property is sold shortly after for significantly more, the tax office may well seek to have the actual sale price substituted for the probate value in the Inheritance Tax account which would yield extra IHT (sale price - probate value x 40%).
If the property is being sold by the estate (as opposed to by you) a significant amount of time after the death of the owner for significantly more than the probate value, then the tax office may not query the probate value and the estate will have Capital Gains Tax to pay on the difference between the probate value (£250,000) and the sale price. If the sale by the estate is within the tax year of death of the owner or either of the next two tax years, the first £11,000 of the gain will be tax free with the balance being taxed at 28%.
If the house in now in your name and it is your main or only home, you should be able to sell it tax free as you will read in HS283 here
I hope this helps but let me know if you have any further questions.