I've dealt with this gooseberry fool a few times before.
As had been mentioned code BR is basic rate which is 20% income tax on everything you earn in that PAYE employment. This is also sometimes called the emergency tax code as HMRC or the employer uses it if they don't know what tax code you're meant to be on for that job (for example you're still doing some other job for a bit such as working out your notice period).
They often fail to update it so you have to request this yourself.
If you are on multiple payrolls / multiple employed jobs you can only apply your personal tax allowance to one of those jobs (most people pick the highest earning for their "main job"). You will be taxed on code BR by default on your 2nd, 3rd, 4th etc jobs and deduct 20% income tax from your gross pay on all of them, I'm not sure about NICs.
There are three ways to claim a tax rebate or an effective one.
You ask HMRC to correct your tax code if you have one job to what it should be, this is referred to as your personal tax allowance code or similar. Ie the normal code. But it'll take time for them to do that and they'll eventually send you a refund as a cheque, if they owe you one, but you generally won't get that until the end of the tax year in which you earned that income.
You can stay on code BR until HMRC notice and they'll change your tax code so that you are paying less or no tax in future years as you earn, effectively paying you back (they can also do this in the other direction to recover unpaid tax).
You can register for self assessment to calculate your own tax liability by looking at your payslips and end of year tax certificate (P60) for all your jobs and adding them up. This means filing your own tax return, even if you aren't self employed. It's often the fastest way to get a refund from HMRC because they can deposit the money directly to your appointed bank account.
You can call or write to HMRC, explain what tax you think you actually owe, and essentially demand a tax refund. If they agree they'll issue you a cheque in the post but it can take a while to reach you.
If you are earning below the taxable threshold (referred to as the tax free allowance) of 12,000 in any given tax year, you shouldn't owe any tax, but because of how the PAYE (pay as you earn) system is set up to prospectively collect taxes rather than retroactively collect them, you often overpay tax if you do multiple jobs, or even simply change jobs frequently.
HMRC also obligate that employers use PAYE and RTI (real time information, every time you get paid HMRC is immediately notified of the amount and any deductions which is recorded against your national insurance number in a government database) for all employees. This means basically everyone is logged with over taxation almost by default if anything goes wrong, which can be your employers fault, your ex employers fault, HMRC's fault, or rarely your own fault if you requested HMRC or your employer put you on the wrong code (so, basically tax evasion).
The system is rigged against people doing multiple jobs, and does what it can to prevent people contracting independently on their own payroll, and it's bullshit.
So, good luck with it all I'm afraid. I'd start with studying the various tax codes, calculating your own personal tax liability, calling HMRC (which anything other than around 7am will have you on hold for half an hour or more), writing to HMRC, or voluntarily registering and filing a self assessment tax return that includes all the jobs you did and what you earnt so that HMRC are effectively forced to pay you back. Which currently means waiting... Erm, if you file by the Jan 31 2022 deadline for tax year ended last April , until April 2022 to get your refund. If its for tax year we're in now, it's 2023
It may be faster to ask HMRC to change your tax code so that you pay no tax and I think it might also be possible to get the refund added to your pay so you get one massive paycheck one month and then they correct it back again to normal.
It's worth bearing in mind both your works HR department or director have to do the right stuff as well as HMRC for the tax code stuff and they sometimes strawberry float it up.
Personally, I would make sure your using your personal tax allowance first, if you have one job, to stop them collecting tax if its below 12k. Then I'd contact HMRC asking for a rebate or if you don't mind waiting file for self assessment and get it that way. That gives HMRC effectively a deadline and a mechanism through which they can pay you back.
That they don't teach our tax system at schools is a strawberry floating travesty, like its not at all important to understand how the government collect and spend your money.
Edit: THIS IS A strawberry floating BOT THREAD FROM 11 YEARS AGO AND I EVEN SAW THE REPORT