Can I get into a top uni for engineering as an A Level Resit?

I got CCC in my A Levels last year and was wondering if I redo them could I get into a good RG uni for engineering. I would be resitting privately. Another question is would I need new predicted grades or can I get in based of my A Level results?

You'd have to make sure it's clear on your UCAS form that you're resitting, I'm not sure about predicted grades. I'm pretty sure that resitting slightly disadvantages your application for some unis but the the vast majority of universities will not view it any differently.
What unis do you plan on applying to?

I was looking at Bristol, Bath, Sheffield, Southampton, Manchester

If you are using your last school for your UCAS reference, then ask them if they are prepared to predict your resit grades, even if its 'we would expect him/her to achieve at least a B grade' within the reference.

I am currently not using my last school. Would it be too late to contact them now? Also, should I just resit my A Levels without predicted grades because I don't have a third party reference either?

You do need a reference - phone the Head of Sixth or Careers person at your last school and ask ASAP.
if they say yes, you will need to 'submit' your application asap so that they have time to then add your reference etc and send it to UCAS before the deadline.

So my school is willing to be the referee but they aren't able to give me new predicted grades. Would that still be an issue? Does it affect my chances?