There is no Income Tax liablity arising from the gift of cash from one person to another.
If you are a UK tax resident, then you may need to consider Inheritance tax implications. Gifts below £3000, can be ignored for Inheritance Tax purposes, gift above this amount will need to be included in your estate for Inheritance Tax, should you pass away within 7 years of making the gift. You can see more information on Inheritance Tax here:
How Inheritance Tax works: thresholds, rules and allowances