Three of the five patients diagnosed with what is thought to be the world's first cases of the new strain are still in hospital.
Prof Nigel Dimmock, a virologist at the University of Warwick, said: "This is just the beginning. You have got a lot of viruses and if you use Tamiflu at the level they are using it, you'll get resistance."
But he added: "The vaccine is coming on, so Tamiflu is a stop-gap. There's no need to panic."
Meanwhile a mutation of the flu virus which has apparently killed hundreds in the Ukraine could reach Britain, experts say.