I was given a cash gift of £6000 3-4 years ago . I opened up an account in my name and have not used the account just in case the elderly aunt that gave me the gift needed it for anything urgent such as an operation.The account has not been touched and still has this amount of money in it.The account has no mention of the aunts name. The aunt has now died and other members of the family state that this gift should be put back into the estate to be shared. Is this the case legally or am I entitled to keep it as this was a gift to me from her. For info the total amount is not effected by british tax laws.

Welcome, Joe, to AMHD. You have a bit more evidence that is germane: the reason she made the gift to you; the circumstances surrounding the gift and what she said. Here is the legal definition along with the site. I don't think you have to budge at all.
A voluntary transfer of property or of a property interest from one individual to another, made gratuitously to the recipient. The individual who makes the gift is known as the donor, and the individual to whom the gift is made is called the donee.

If a gratuitous transfer of property is to be effective at some future date, it constitutes a mere promise to make a gift that is unenforceable due to lack of consideration. A present gift of a future interest is, however, valid.

Rules of Gift-GivingThree elements are essential in determining whether a gift has been made: delivery, donative intent, and acceptance by the donee. Even when such elements are present, however, courts will set aside an otherwise valid gift if the circumstances suggest that the donor was, in actuality, defrauded by the donee, coerced to make the gift, or strongly influenced in an unfair manner. In general, however, the law favors enforcing gifts since every individual has the right to dispose of Personal Property as he or she chooses.
Gift legal definition of Gift. Gift synonyms by the Free Online Law Dictionary.

I don't know how it works in the UK - but in the US a gift freely given belongs to the person who received it.