thank you. There is generally in English law no presumption of a gift when somebody give something to somebody else but there are certain narrow categories of relationship where a presumption of a gift does arise which includes father and child.
As such, there would be a presumption that the transfer of the property to you amounted to a gift unless you are able to prove otherwise which may not be an outcome which is desirable from the point of your capital gains tax.
In terms of capital gains tax, if you have not been living at the property for the entire period since your father transfer the property to you, capital gains tax would apply for any periods you have been absent from the property unless you own more than one property and made an election to HMRC nominating the property as your main residence which I will assume you have not done unless you tell me differently.
As such, if you decide to sell or gift the property to your mother, this would amount to a disposal for capital gains purposes and there would be a capital gains tax assessed on the increase in value of the property as between the transfer into your name and the date you transfer it to your mother based on its market value whether or not you sale or gifted to her. As such, it may be that transferring it to your mother may not be the most tax efficient decision to make.
The position would be different if you were able to show for example that your mother was given a right of occupation in the property because this would potentially allow you to apply for relief in respect of capital gains tax but from what you say, this was not the case.