Update the address on your driving licence
Update the address on the vehicle logbook V5C
If you pay by Direct Debit for vehicle tax, phone DVLA on 0300 790 6802 to update the address.
It isn't the fine which is the real worry (whoever heard of anyone being fined for that) but the fact that documents about PCN may not reach you and your car could get uplifted by a bailiff.
Yours frugally
Mr Mustard