Manchester can use your UCAT score in 2 ways: firstly they take those who have got a score that is in the top third nationally and invite them for interview straight away. They also invite some for interview by taking a holistic approach: so they consider your UCAT score with your NAI, GCSE grades and widening participation.
The second way allows applicants that may not have got an excellent UCAT score a chance by considering other aspects. Looking at previous years, a score of 580 generally won’t fall into the top 1/3 so if you were to apply you’d be looking at getting in via the holistic approach. Your GCSE grades are good, however, I think it’s only worth considering the holistic route if you are eligible for widening participation. The uni don’t give much information on how they weigh the different elements for the holistic assessment, so it’s ultimately up to you to decide whether you want to sacrifice an application to Manchester knowing that it might not be successful.
For a score of 510 I recommend looking into these med schools: Cardiff, Queen’s Belfast, Keene, Plymouth and BMAT unis.