The gift of cash in this way does not have any income tax implication for the recipient. However you should make the family member aware of the Inheritance Tax (IHT) implications which apply. You can gift £3,000 per annum without any issue to IHT. In addition,the £3,000 allowance can be carried forward from a previous year if unused, making up to £6,000 IHT free.
The balance of the gift is called a potentially exempt transfer (PET). This means that if the donor dies within 7 years there may be tax payable by the donor’s estate. Tapering provisions apply so the longer the donor lives the less the potential tax.
The two extremes are that gifts made "on the death bed" are fully taxable, but gifts where the donor survives 7 years are not taxable. In addition, to the £3,000 per annum exemptions there are specific exemptions for normal expenditure out of income, gifts on occasion of marriage, small gifts, gifts to spouses and other specific gifts.
The rules are very complex and if you are the donor, you should seek specialist advice from your local TaxAssist Accountant. The answer also assumes that the donee is not an executor or trustee of the donor's estate. If he is, specialist advice will be required, as the answer will change.