I have mentioned these before but here are some links.
Oxford University run taster courses in the summer term but you need to start thinking about. Applications open in January. You need to be a credible Oxford candidate - ie some A*s at GCSE and likely to be As this year. I can write references but you'd better see me. Asking me with a day to go isn't helpful! http://www.uniq.ox.ac.uk/content/2014-application-information
It's the same with Sutton Trust - applications open in January. Most people who get onto their courses will be the first generation in their family to go to university. Look at the eligibility criteria. http://www.suttontrust.com/students/uk-summer-schools/application-process/
If you don't fit with either of these, you could try Googling for other options. They are bound to be there.
