You need a UK address to have UK car insurance as the insurance premium is dependent on where the car is mostly kept. However you do not necessarily have to live at this address.
You do not need a UK address for an MOT certificate but you need insurance (and thus an address) as well as an MOT certificate to get a tax disc
(As far as the UK is concerned, there is of course nothing to stop you from insuring and registering the car in Berlin or similar as long as the car is roadworthy and legal).