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On the basis that there is no Mortgage on the property which is being transferred to you, there won't be any Stamp Duty for you to pay as there won't be any consideration being paid for the property. Neither will there be any other tax for you or for the party transferring the property to you, to pay.
The only tax impliccations are as follows-
As you will own 2 properties, you will need to elect which property is your principal place of residence for Capital Gains tax (CGT) purposes. CGT is payable on any sale of the property which is not your principal place of residence if it has increased in value from the date you acquired it. In the case of the property which is being transferred to you now, you will be treated as having acquired the proeprty at the current market value. This scenario also applies to your family member if they currently own 2 properties and the property they are transferring to you now is not their principal place of residence.
The only other tax implication is that for Inheritance tax (IHT) purposes, if your family member dies within 7 years of making the gift to you, the value of the property or a percentage of it, depending on when during the 7 year year period they were to die, will form part of their Estate when calculating if IHT is payable. If the family member is not married, they have a tax free Estate for IHT purposes of £325,000.
I hope this gives you the tax overview. However, please let me know if you require any further clarification.