If you can afford it, get a private tutor, someone who does functional skills, then do the GCSe afterwards. If you're paying them, you can demand a standard of behaviour and also try a few to see who has the best method/style for you.
I recommend doing it because as you said even jobs like part-time retail or restaurant/fast food work or call centres, these days ask for your GCSEs and all the grades listed, your A-levels and the grades and then degrees (depending on role). So it's very hard to get even a weekend job without having your GCSE grades and having at least decent if not high and competitive ones - the same for A-level.
Although, as I said earlier, older people (40s+) are able to get away with it because they have often decades of experience, say they've lost the certificates, or they can not remember their grades. Younger people (16-30 and even sometimes 30-40) have no chance of that, as expectations of applicants are changing - just think about how much longer the job application process is nowadays. The NHS isn't short of applications (it's more of a retention issue than recruitment) and they aren't going to wait for someone to do a GSSE in maths when most of the applicants will have it already. All healthcare professional roles (doctors, midwife, nurse, PA, nursing associate, speech and language therapy, dieticians, and more) need at the very least A-levels and most of the time degrees. So to get into 6th form and the days university, it's impossible to do so without good GCSEs and bare minimum: English Language and Maths GCSE. Unless you do an acess to higher education course (normally mature students, nothing younger people, they're expected to go back and do GCSEs). You also often need a good overall set of GCSEs and high A-levels for such university degrees these days. So even if you aren't directly asked on a job, if they ask for your general education and you say 10 GCSEs, 3 A-levels (that is mentioning it and most these days ask for proof as well and the speicifc grades).
They rely on the system working to check that you have the right grades.
6th forms check GCSE grades, university to check A-levels and GCSE grades, and so on.
London universities in my experience are very strict with GCSEs, I know LSE and UCL and Imperial in particular like higher GCSEs often at a 6 or 7 minimum (B/A) not just a C.