Quote From Ferum:
currently my funders seems to approve on Cambridge, oxford, imperial and manchester only.... which is better on anyone opinion ...looking for supervisor 1st then taking their topics...or we giving out our topic to supervisor for consideration ? thanks in advance..
Well if you can get in to any of those they are good universities. Imperial is very famous for engineering above all other subjects. I would look for a PhD that suits you rather than starting with trying to find a supervisor. The topic you study is very important as if you don't like it the PhD can feel very long and boring.
visit the uni websites, use findaphd.com and choose your favourite topics at any of the universities. Then apply for all the ones that interest you. Hopefully one of them will give you a place on their PhD programme.