What type of engineering are you interested in?
The big ones are Mechanical, Aerospace, Electrical&Electronic, Chemical, and Civil. Alongside that you have Materials, Systems, and Naval. You also have General which will cover the big ones in your first couple of years then you will specialise later.
In terms of unis, look for unis with a large engineering faculty rather than just what rank a uni gets for that subject, e.g. somewhere like Swansea which has a big engineering focus will outpace a lot of other universities with higher rankings. Don't worry too much about grades, whether you've got ABB or A*A*AA, some universities at the bottom of that band of requirements will produce just as high quality graduates as those at the top. Also don't focus on Cambridge or Oxford if you're interested in a specific discipline of engineering, there's no point in going to study general if you know you want to do a certain discipline as you just won't get the same exposure to it, and you will need to push through disciplines you may despise on top of that.