Private candidate exam centres for A-levels near West Yorkshire/leeds?

Any centres near west Yorkshire/leeds. Woodhouse grove is out of the option for me as I am aged 20-21 and the school isnt for anyone over age 18 and the only other somewhat close one I found is tutors & exams in doncaster.

Is there any other possible centres?

It depends on which exam boards you want to do your subject under. Not all exam centres are approved by all exam boards, so you would need to check.

If you can specify the subject and exam boards that you wish to do them under, I might be able to help you more.

The subjects I want to do: Maths, Further maths and physics

Exam boards: Edexcel for maths and FM and AQA for physics.

AQA: It's funny that you say Woodhouse Grove is not an option since they accept private candidates. See:
https://www.aqa.org.uk/student-and-parent-support/private-candidates/finding-a-school-or-college#yorkshire_66819

EdExcel: if you go to the following page: https://qualifications.pearson.com/en/support/support-topics/understanding-our-qualifications/where-can-i-take-edexcel-exams.html, you would see a link for the following site: https://www.jcq.org.uk/private-candidates/
Using Woodhouse Grove's postcode as a proxy, surprisingly it's also an approved exam centre for EdExcel for private candiates. See:
https://www.jcq.org.uk/private-candidates/?user-postcode=BD10+0NR&user-lat=53.8401477&user-lon=-1.6986514&qualification-type=gce&awarding-body=pearson&gce-subject=71
https://www.jcq.org.uk/private-candidates/?user-postcode=BD10+0NR&user-lat=53.8401477&user-lon=-1.6986514&qualification-type=gce&awarding-body=pearson&gce-subject=50

I don't know the specifics, but you should contact Woodhouse Grove to double check on whether they are willing to take you on as a private candidate.

If you have any further questions, let me know.

Contacted them earlier today (no response yet) but my main concern is my age. The school is for people aged up to 18 but Im 20/ going on 21 which is my concern

They have a separate part of the school for private candidates. You're not going to be mixed in with the other students - that would pose too much of a health and safety issue.