If the bike has been notified to DVLA as being a 'write-off', it will have to undergo a Vehicle Identity Check, to see if it's still essentially the same bike. If it passes the test (which is based on a points system), it can retain the same registration. However, if it fails the test it will have to be re-registered with a 'Q' registration mark. In order for this to happen, it would need to be taken to a vehicle testing station, to seek a Motorcycle Single Vehicle Approval certificate.
See here
http://www.direct.gov.uk/en/Motoring/BuyingAnd SellingAVehicle/RegisteringAVehicle/DG_4022486
and here
http://www.direct.gov.uk/en/Motoring/BuyingAnd SellingAVehicle/RegisteringAVehicle/DG_1001419 9
Once you've persuaded DVLA that the bike should no longer be regarded as a 'write-off', with or without the original registration, you can start to deal with all of the usual matters such as tax, insurance and MoT. You might need to seek out an insurer who provides cover for 'kit bikes' (especially if a Q-registration is issued). Specialist biker magazines are probably the best place to look.
Chris