The quality of your institution will probably be taken into account by anyone reading your application; if you got a first from somewhere low tier then it would not look better than a high 2:1 from Imperial. When people say you need a first to do a PhD in string theory, they arent talking about scraping a first with 71% from a midtier university, they are talking about either a first from a top university, or a very high (80%+) first from somewhere mid-tier.
Also note that it works both ways; should someone who got 68% from Cambridge be preferred to someone who got 72% from Imperial? The gap there is probably about the same as from Imperial down to Warwick/Edinburgh/etc, look at the entry standards here for example:
http://www.thecompleteuniversityguide.co.uk/league-tables/rankings?o=Entry&s=Physics+%26+AstronomyAlso, it wont just be about your overall mark, people will also look at
a) what modules did you do well in? Courses like string theory are heavily mathematical so if you got a high first in the more advanced mathematical modules, this will probably look better than getting high marks in first year mechanics
b) what is the trajectory of your grades? Did you get a low 2:1 during your first 2 years, and then step it up for the (most important) later years? If you get a good first for the final year of your course then that looks great.
c) what is the quality of your projects? The biggest one is your MSci project so if you have got a high grade in that and can get a good reference from the supervisor, this looks good.
d) have you had any summer research experience?
etc