An unlimited amount really. However if you were to die within 7 years of giving the money, then the gift would be considered as part of your estate for inheritance tax purposes.(the amount does decrease depending on when you die within the 7 years.
You can give a small amount of money (�100 i think) to however many different people you like within a tax year without afecting your inheritance tax status as above. I believe you can also give money to a son or a daughter when they get married.