Laurence Oliver died in 1989, just as Kenneth Branagh was launching the film of ‘Henry V’, which he wrote and directed and in which he starred.   The coincidence made some journalists, especially in the U.S. wonder whether Branagh as the new Olivier.   

Then, when Branagh’s performance was nominated for the annual awards at the end of the year he seldom looked like being strong competition against Daniel Day-Lewis. 

  For ‘My Left Foot’ this second young British actor swept all before him.   That is not to say that Day-Lewis is the next Oliver, for which over the years there have been many failed claimants

Certainly it does not look likely that Day Lewis will seek greatness on the stage, as Olivier did.   But it would seem that we have a chameleon, one gifted with sensitivity and authority. 

  Because of his looks and the Oscar won while so young he may become a leading romantic actor in Hollywood – of that is what he and Hollywood want ( and with the British film industry in its depressed state let us at least hope he will dazzle us with his versatility from there).   But the closest analogy with Olivier is one that both actors probably would appreciated – that other actors are in awe of him”. – David Shipman in “The Great Movie Stars – The Independent Years”. (1991).