Hello! I hope you had a lovely time at your summer school! I went last year and had the time of my life, now super excited to be heading to Durham this September. In terms of your question, 100% apply. Last year the contextual offer was guaranteed and I'm 99% certain that this meant that everyone got an offer (which should also be 2 grades lower) no matter what (this doesn't mean don't put effort into your application though!). I obviously don't know how the system works exactly, but from how I interpreted it we were guaranteed an offer two grades lower, rather than guaranteed that our offer would be two grades lower if we achieved it (I hope that makes sense lol). I can't promise anything, and it might have changed since last year, but its still definitely worth applying. If you are determined and dedicated throughout the next year you may well exceed that offer. Don't limit yourself, its not bad to apply above your predicted grades for one uni, especially as this one is likely to accept you. As someone has already said, make sure to apply to secure backup unis and have one you feel confident achieving as an insurance. But other than that, if you want to go to Durham, go for it!
I hope that helps you and I wish you the very very best of luck. Let me know if there are any other questions I can help you with!