Going to University isn't all about going to a place with a prestigious reputation. Unless you want to go into a profession that solely looks into what University you went to, then most of the time an upper second class (2.1) or above BA degree from any University is what's most important (that's if you want to progress to MA level or a L7 equivalent, or want to apply to a job straight after). Furthermore, depending on what you want to do career wise, some work experience in your relevant subject/career field is also important.
Lastly, regarding your GCSE's and A levels: You have grades 6-9 in everything, and top A level grades. This means that you can pretty much apply to anywhere (in most cases).
So apply to wherever you wish to go and see what happens. What subject/course are you thinking about taking?