1) it wasn't up the avro to decide if they needed a better bomber, the government asked for it
2) the use of halifax's and stirlings would show the need for a better bomber...................
The thing was, the RAF considered the Manchester to be a heavy bomber. If the engines had worked I don't think neither Avro nor the British government would have considered installing the four engines to make the Lancaster. Even if the British government decided they needed a better heavy bomber, I doubt it would had the appearance of the Lanc. It probably would have been something else all together.
I think they would have, knowing British military mentallity, they do stick to a good design when it's needed, and they are also trying to cut costs (even in war time), designed off something that is already there benefits them, greatly.
Possibly, the British did develop some outstanding aircraft out of some flops. But I'm not sure they would have taken a good aircraft (the Manchester if the engines worked) and try to substantially improve it. Assuming the Vultures worked I think the RAF might have tried mounting four of them and producing a bomber of B-29 type proportions.
The Vulture WAS a Rolls Royce engine, so was the Peregrine, were they "brilliant?" It is true that Rolls Royce had two brilliant success with the Merlin and the Griffon, but they (like most every company) had as many flops as well.