I haven't done a master's in accounting, but I have done a bachelor's in it (shamefully).
To become an accountant, you would need the appropriate professional accounting qualification for the role you want (this is different in the US and Canada where you need to have done a degree with sufficient accounting classes to do their respective CPAs). You cannot become a qualified accountant through a degree alone (unless you're heading to a middle eastern country where you might be able to get away with just a degree).
A master's degree is not necessary and is often more expensive than doing the professional accounting qualification directly. From a master's degree, the most number of exemptions that you can get from any professional accounting qualification is 9 (out of 13-15 modules in any one professional accounting qualification), if you picked all the relevant electives that gives you the max number of exemptions (you will need to use the exemptions calculators on each accounting body's website to confirm the electives you need to take to do this).
In contrast, should you go out of your way to fund all of your accounting studies (and presumably pass everything first time), you should be able to complete all your studies in 2.5 years at £5000 (assuming you take 2 exams per cycle, and you take exams in all 4 cycles per year). You should not ever need to do this because your employer would be able to fund a good portion of this.
In other words, going straight for the professional qualification not only is cheaper but faster than doing any degree.
The entry requirements for virtually any accounting qualification is passes at A Level or equivalent e.g. AAT Level 3, BTEC, IB, whatever.
There are dozens of professional accounting qualifications for the UK (
https://en.wikipedia.org/wiki/British_qualified_accountants), and a number of these are recognised abroad (if they are directly recognised, you can get them converted).
However. you would need to be aware of several distinctions between the types of accountants:
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public sector accountant - work in the government department
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management accountant - work in organisations providing accounting services, which can include the public sector
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private accountant - work in practice
Public sector and management accounting qualifications would specifically allow you to work in those specific areas, whereas a qualification for a private accountant can work in all 3 areas. See the following:
https://nationalcareers.service.gov.uk/job-profiles/management-accountanthttps://nationalcareers.service.gov.uk/job-profiles/private-practice-accountanthttps://nationalcareers.service.gov.uk/job-profiles/public-finance-accountantIf you want to only go into management accounting, I recommend CIMA.
If you want to only go into public sector, then I recommend the CIPFA.
If you want to go into private practice (or want something very flexible) but stay in the UK only, then I recommend ACA, ICAS, or CAI. ACCA is good if you intend to work in 180 other countries without the headache of doing a lot of paperwork to qualify in any country. There are other accounting bodies, but the above are the most popular.
With any accounting qualification, you get the study component that you would need to do, and then you need the relevant professional accounting experience (usually 3 years) to completely qualify. The accounting study will take you from first year degree level when you start to master's degree level upon completion (and the qualifications would be the equivalent of a master's degree, but you generally can't use it to apply for PhDs in accounting as far as I know).
If you want to join a grad scheme in accounting, you're more than qualified to do so (they accept grads from any degree at particular grades, mostly due to the requirements of the professional qualifications). However, it's likely to be ridiculously competitive the larger the firm you target (it's an industry hinged on reputation) e.g. 1000 applicants for 1 grad position at a Big 4 company. There's less competition in the medium and smaller firms, but you might not likely to be so readily be able to get a job if you leave them.
The key thing any employer is looking for is relevant work experience (the chicken and the egg argument about can't get work without experience). If you don't have this, make sure you have stellar grades (especially at A Level) and a very very good cover letter/personal statement, showcasing your absolute enthusiasm for the job. Otherwise, you would need to do a lot of networking.
Having an accounting degree is very very unlikely going to sway the opinions of employers over the competition of other candidates. They usually care more about the character and experience of the individual candidate over the qualifications that they have.
The only time when a master's in accounting is in any way relevant is if you want to do a PhD in accounting.