There are 2 separate issues here. Neither of them relate to Capital Gains tax.
1) Inheritance Tax .An individual can give away certain amounts per year - up to �5k - to another individual, free of any clawback for IT. The individual can give away more than this, but it is known as a Potentially Exempt Transfer (PET). This means that the individual must live for at least 7 years from the date of the gift, otherwise there may be a clawback of IT - it depends on the overall value of the estate of the person on death. See more about it here.
http://www.direct.gov.uk/en/MoneyTaxAndBenefit s/Taxes/InheritanceTaxEstatesAndTrusts/DG_1001 0612
2) Payment for care homes
Local authorities that pick up part of all of any bill for someone in care take a dim view of relatives taking the benefit of assets being given away by the person in care. It is very possible that the local authority may question why 50% of your Nan's assets are given away in this manner, if the funds are needed for payment for the care.