To the best of my knowledge it is not an legal obligation to carry proof of identity immediately on demand.
It is unwise to carry your driving licence, motor insurance and all credit/debit cards in case you lose them all in wallet(s), purse(s) or, as pointed out earlier, your car is stolen.
Think of the time and inconvenience it will cost in reporting the losses and replacing these. This applies not only to you but the issuing bodies.
Carry the minimum valuable cards/documents outside your home where they should be kept in a safe place.
SIQ.