If your mother is gifted or given a property by her relative, she will be deemed to have acquired it at its open market value at the time of the gift. That market value will be her "cost" for Capital Gains Tax purposes so if she sells it for a similar sum there is unlikely to be a taxable capital gain. She can deduct expenses she will incur when you sells the property (legal fees, selling agent fees etc) from the disposal proceeds.
An individual can make tax free capital gains in any one tax year of £11,000 so your mother would need to sell the property for more than the sum of the market value of the property at the time of the gift, the £11,000 Capital Gains Tax exemption and the disposal expenses before she needs to concern herself with CGT.
As far as the relative is concerned, unless the property has been their main home for the whole period of their ownership of it, they may have Capital Gains Tax to pay as they will be deemed to have "sold" it to your mother at its open market value which will probably be higher than the price the relative paid for it when they bought it. This tax treatment will apply if your mother and her relative are "connected" for tax purposes. The definition of "connected persons" is here
. In addition, as you will read here
, if the transaction is not between connected persons but is a bargain not made at arms' length, then the market value rules can still apply.
I hope this helps but let me know if you have any further questions.