You firstly need to make sure that your domain is not "locked" with your current registrar (contact them for details on this) and can then initiate the transfer. An email will be sent to the administrator and registrant contacts currently shown on the domain (so make these addresses are valid) which must be replied to to confirm you wish the transfer to take place.
Once this stage is completed, transfer can take anything from 12 to 72 hours - it all depends on the losing registry.
UK transfers work differently than usual transfers and therefore a little more work must be put in. After putting in the transfer request, you need to contact your existing registrar and request that the "retag" the domain name to: ENOM
Without this tag transfer, the domain simply will not move over. Once done however, transfer is somewhat faster than the gTLDs and should be completed within 24 hours.