Imperial, Southampton, Loughborough, Birmingham, Manchester, Oxford, Cambridge all worth considering.
I'd note that while Cambridge is a "general engineering" course, you do functionally have to specialise from third year onwards in one particular area (particularly if seeking accreditation for your degree - as they do offer specialisms with the associated accreditation as a "single subject" engineering degree elsewhere has) and the "general" courses taken in the first two years more or less mirror the other areas of engineering you'd often have to study in a mechanical engineering degree elsewhere anyway. Same for Oxford.