They're all a very similar par. Manchester is below that par, Cambridge and Imperial don't accept BTECs.
Go Leeds if you like the mechanical/manufacturing side, go Bristol if you like the electronic/control/programming side, go Bath if you want a year in industry, go Southampton if you want space. Alternatively, apply to all of them, you have 5 spaces...
Honestly, prestige has basically no effect on reputation of an engineering degree. I remember when I was starting my degree (so 4 years back) that Bournemouth's Engineering course had 100% employment prospects, even now it's prospects within engineering happily compete with the best. Use unistats to get an idea of degree prospects, not rankings, as unistats gives a much better overview of the situation. 90% of grads being employed isn't much use if only 30% go into Engineering related professions, compared to somewhere with 80% employed but 60% are in Engineering.