Getting into Cambridge is very competitive and they might well look at your Maths and Science grades as part of your overall application. For Psychology in particular many have Maths GCSE requirements. Bath as an example requires grade 7 GCSE Maths. For other courses which are not so Mathematical the GCSE requirement is often not as high.
Psychology is a difficult subject to advise you on. Some universities require 2 sciences. Others 1. Some accept A level Psychology as a science and others dont.
Sociology doesnt usually have the same science and Maths requirements.
Your only option is to check the entry requirement for each university you are interested in. Check for both subjects what are the requirements at A level and GCSE Maths. Use this link to help you.
https://digital.ucas.com/searchHere is the entry criteria for Birmingham for Psychology. They accept students taking Psychology as a science and make a lower offer. You will need to check regarding your Maths and GCSE sciences.
A level - AAA - AAB
Entry requirements of AAB apply if one of the following subjects are being taken: Chemistry, Biology/Human Biology, Physics, Psychology, Math/Further Math or Statistics. Specified subjects excluded for entry: We do not accept General Studies, Critical Studies, Critical Thinking, Science in Society, World Development, Communication and Culture, Citizenship Studies and Use of Maths.