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As your parents are transferring the house to you and your wife, they will be liable for capital gains tax based on the value at the date of transfer less the value at the date they acquired the house from your grandfather's estate. Assuming the house is presently in the name of both of your parents, they will have an annual allowance totalling £22,200 which can be deducted from any increase in value before the tax rate is applied. So for example if they acquired the house at a value of £100000 and it is now worth £180000, they will pay CGT on the increased value of £80,000 less £22,200 = £57,800. So they each have a net gain of £28,900. The basic CGT tax rate is 18%. If either of them are higher rate taxpayers they will pay CGT at 28%. Neither you nor your wife will be liable for CGT and you don't own the asset. I hope that helps. Please leave a positive rating so that I am credited for my time.
The CGT is payable based on the VALUE of the asset transferred less the VALUE at acquisition. That applies whether money changes hands or whether the asset is gifted for no money. If your parents can't fund the tax then they should not make the transfer. There is thing called gift relief but it only applies to business assets, not to the situation that you describe.
Your analysis is entirely correct. If they elect to gift an asset they will pay CGT in the usual way even if they make no money. That is because CGT is paid on a DISPOSAL of an asset even if the disposal is not a sale. The only exceptions are transfers between spouses and the gift of business assets. In your scenario there is no alternative solution.