To send a domain transfer, login to your Nominet account associated with that domain name, then click on the registrant transfer link, enter the domain name and confirm it.
Next, enter the buyers email address, under that, there are 2 buttons, one is ticked if the buyer is paying the transfer fee of £10 + VAT, the other to be ticked if you are paying the fee, tick whichever applies (the buyer usually pays the fee unless you have stated otherwise during a sale), then click submit.
The next page will show details of the transfer, if they details are correct, tick the box and then submit.
The next page will confirm that the transfer email has been sent to the buyer. When they receive the email, it contains a link to Nominet for them to complete the transfer.