I assume that you own the property jointly with someone else, and want to put the property into their sole name.
I assume that they are in agreement with this.
I assume that you do nor want or need any advise on how much, if anything, you ought to be getting for your interest in the property.
1. You will need to have agreed with the other person that they are to become the sole owner, and what. if anything, you will be paid for your share in the property.
2 The mortgage company will need to give its agreement. They will only do this if they are satisfied that the other person can afford to pay the mortgage without your help.
3. This will involve a formal application to the mortgage company, filling in any forms they want, and paying whatever fees they ask.
(Alternatively the other person may choose to remortgage with another company in which case he/she will have to make an application for that new mortgage.
4. Once everything is agreed you will need to prepare and execute a land registry form TR1 and send it to HM Land Registry with their fee which will depend on the value of the property.
This is a very simplified answer, and more information from you may enable a more refined answer to be given.
Lawyers are never needed, but are often useful.