I would contact the mortgage lender to find out what the procedures are to undertake your request. All financial institutions have different procedures, but it is certainly possible.
My mum was a guarantor on my first mortgage, as I was 18 years old when I got on the property ladder. After a short while, I decided that I would like to have the loan account in my own name and own right and contacted my lender at the time (Yorkshire Building Society). They took the instruction from both me and mum in writing, along with some pay slips of mine and bank statements to prove that my financial standing had not altered in any way.
The procedure was quick, striaght forward and painless.
However, this procedure was done some 6 years ago now, and I daresay that it is not the same! Contact the lender for more advice.
Regards,
STAH