Are you using a solicitor for your divorce?
If so then they should be able to do it with the divorce I'd have thought.
If there is a mortgage on the property then that will need to be sorted and consent from your lender would be required unless the mortgage is being full paid off on the transfer.
If it is anything other than a simple transfer, no mortgages involved etc..., use a solicitor.
If simple then you can get a form TR1 from the Land Registry website and send it completed and signed to the Land Registry (office finder also on the site) with the �40.00 fee.
http://www.landregistry.gov.uk/
I would probably charge between �75.00 plus VAT and �150.00 plus VAT depending on what needed doing with regard to mortgages.
There would also be the Land Registry fee payable (�40.00) and the solciitors would probably charge for getting copies of the title (�3.00 per register, �3.00 per plan) and any other appropriate documents and, if there is an old or new mortgage, TT fees and Land Registry searches (��3.00 per title and �2.00 per person to remain on the register).