Oxbridge Maths Gap Year Confusion

I'm finishing A Levels this year and have realised that I applied for the wrong subject this year. I will be most likely applying to unis again on a gap year this time round but this time for maths.
I would like to apply to oxford or cambridge (more likely cambridge) but I hear that doing a gap year and applying for maths there is a big no no. I plan to tutor students at A Level maths/FM, sit STEP and AEA as well as working a part-time job. My question is: How big of a disadvantage am I at for doing this vs applicants in year 13 who are applying?
I am confident that I could score well in the MAT or TMUA but I may consider not even applying there and following this particular plan if my chances were really low.
Any responses are appreciated, thanks.

i didn't apply for maths, but my friend did this year (for oxford - rejected unfortunately) but her teachers gave her lots of advice on taking a gap year for oxbridge.
in general, they don't really like it because it will have been a long time before the start of the 2022 course since you did any maths, but, since you're doing a lot of extra work to do with maths, i think it should be fine; i think it's also quite important to keep testing yourself on a level/fm content & they need proof that you will be doing that.

but, if maths is your passion, absolutely go for it. there's no point in doing a degree you don't want to do because you don't think you'd get into oxbridge - there are plenty of other unis out there who would love to have you if oxbridge decide not to offer you a place.

thanks, I'll take that onboard. I'll be practicing consistently and hopefully that's incentive enough for tutors to see that I'd be a solid choice.

Oxford is neutral to deferred entry applications in maths. The deferred entry policy is online in the faqs page.

Found it thanks, very useful.
Also I'd be interested to see whether Cambridge have the same attitude...

See section 7 of https://www.maths.cam.ac.uk/undergrad/admissions/files/admissionsguide.pdf