Hello,
Yes, definitely apply! Reading considers everyone really highly, it doesn't just consider grades but also your personal statement, work experience or experience and your interview (if you have one!). There is also no longer a cap on the number of students that a university can take which gives you even more chance of an offer!
I study a different course to psychology but my predicted grades were BCC (for an ABB course), and I still got an interview which led to an offer! This was because I had a strong personal statement which showed my extra-curricular skills and work experience - so when applying put down any experience, interests or volunteering you have and you'll have a great chance of getting an offer! The university will also be able to see that you were close to an A in your subjects which gives you even more chance! Even though that's my own personal experience, and everyone's is different, you do get 5 universities to choose from when applying, so having one or two risky universities won't change your options too much and could even work out for the best!
Good luck with your application and feel free to ask anymore questions,
Amelia, Second year studying Archaeology and History at Reading