GCSEs in Uni Applications

How much are GCSEs weighted in uni applications (specifically for Oxbridge/RG unis)?
I did higher and passed all my subjects, however some grades were lower than what I was predicted due to some extenuating circumstance (I know that this will be considered but I’m still wondering)
Especially with courses that are more quantitative (in this case psychology)
I know the grade requirement is usually a grade 6+ in maths but will an applicant be at a very big disadvantage if they got a grade 5 (higher tier) due to certain circumstances/restrictions from school?
Especially if taking A levels such as biology and psychology that have elements of maths (and being predicted A*)
Also, if the applicant decides to work on said math skills + even picking up things such as computer science in their own time to build up these skills (but not taking any official tests via school) is that favourable (if mentioned in personal statement/reflected in admission tests/interviews) or not really considered?
Would this still be an issue?

GCSEs are automatically given great weight in the Oxford filter. This is because it uses a computer generated number that is based on your GCSEs and Entrance Exam.
For Cambridge, they will look at your entire application. A low maths score for GCSE when taking psychology will certainly raise eyebrows, so make sure to evidence the extenuating circumstances. Better scores for for mocks (your teacher can write your specific stats in) and any other independent assessments will really help you.
If all else fails, I’m afraid it’s a “take a gap year and apply with real A-Levels” situation - in that context, GCSEs mean almost nothing.

I know the grade requirement is usually a grade 6+ in maths but will an applicant be at a very big disadvantage if they got a grade 5 (higher tier) due to certain circumstances/restrictions from school?

Especially if taking A levels such as biology and psychology that have elements of maths (and being predicted A*)
Also, if the applicant decides to work on said math skills + even picking up things such as computer science in their own time to build up these skills (but not taking any official tests via school) is that favourable (if mentioned in personal statement/reflected in admission tests/interviews) or not really considered?
Would this still be an issue?

I suspect universities will take the view that you could have retaken maths GCSE to get a higher grade while doing your A-levels. My understanding is that not meeting the minimum GCSE requirements for a course is likely to result in a speedy rejection.
If you arrange to retake GCSE maths, you simply list it as a pending qualification on your UCAS application, and a university (if they make an offer) will make it conditional on the GCSE result as well as your A-level results. A suggestion I've seen is to retake maths in the November exams as that revision won't get in the way of revising for A-levels. (Of course this assumes that you're in year 12 at the moment.)
I would check with the Admissions teams at the universities you're considering studying at to get their perspective. That way you can avoid applying to universities which will immediately reject you for not meeting their GCSE requirements.

Do check the individual universities course pages very carefully for specific requirements around GCSE - for the majority of uni's a grade 5 would be perfectly acceptable, some require a grade 6 or above, some (like Oxford which has a high maths component to the actual degree) expect a grade 7 or above. Remember not all unis that are ranked highly for psychology are RG!! ( Bath, for eg., which has a grade 7 Maths requirement) if you are considering Oxbridge then you need to discuss with your careers advisor/tutor as I suspect your GCSE's may not score well with Oxford at least (and the course may not be your cup of tea either ). GCSE requirements are sometimes set in stone ,whether or not you have extenuating circumstances.

Did you have extenuating circumstances taken into consideration/ raised with the exam board at the time?

Nope ☹️ Now I’m kind of worrying about that. It’s linked to a diagnosis I’m in the process of getting so idk how that would work.

All uni’s will have an extenuating circumstances policy - for eg. here is Oxford’s https://www.ox.ac.uk/admissions/graduate/application-guide/qualifications-experience-languages-funding/extenuating-circumstances. Here is a summary if Cambridges’s https://www.undergraduate.study.cam.ac.uk/apply/how/disrupted-studies . If it’s something like late diagnosed ADHD or other learning difficulties for which someone is now medicated / given exam adjustments then I can understand the problem but for other things it may be down to why it wasn’t seen as extenuating circumstances at the time, I suppose!