Postgraduate courses help

Hi all,
I want to make a career change to an accountant, from my current position as a junior economist in the civil service. I'm pretty confident about this transition and its future prospects. I am also strongly considering a postgraduate degree in MSc Accounting & Finance, which seems to make the most sense for me at the moment, where previously I hold a BSc Economics from a non-RG uni.
I've applied for Queen's University (Belfast) and Cardiff, but I've just been rejected from the former on the grounds of academic requirements. Will continue to apply for other unis.
Does anyone have any advice they can give me? I guess firstly how does one get into accounting with little experience, and if a master's degree helps, which one is the best? Despite achieving a First for my BSc, I'm worried that it still may not be enough to meet their criteria as I don't come from an accounting background.

If you have done any research into the role, you would quickly find out that you won't need a degree to go into accounting in industry (for academia, the degree is required). If anything, it would be a lot slower and more expensive to do things through a degree. Most graduate employers would be fine with you just having your degree, so long you jump through their other hoops.
I've applied for Queen's University (Belfast) and Cardiff, but I've just been rejected from the former on the grounds of academic requirements.
Most standard MScs in accounting generally won't have any requirements for any specific subject and you should be more than fine if you have at least a 2:1. Queen's and Cardiff are particular MScs where they require you to have prior degrees in accounting/finance (or sufficient coverage of either subjects); these degrees would typically help you to progress onto accounting research and aren't what you would be looking for.
I guess firstly how does one get into accounting with little experience, and if a master's degree helps, which one is the best?
Apply for an entry level role, be it as a graduate or as a junior accountant.
A master's degree won't give you any advantage over anyone with a degree in any other subject or who have just left school, if it's to work in industry. The key thing is that you have high A Level grades, since passing A Level is the main requirement of all professional accounting qualifications e.g. ACCA, ACA, ICAS, CAI, AIA, CIMA, CIPFA. Entry requirements for accounting roles in other countries (other than the US and Canada) tend to be similar.
Despite achieving a First for my BSc, I'm worried that it still may not be enough to meet their criteria as I don't come from an accounting background.
If you look at the profiles of accountants from any accounting firm or accounting role, you would quickly find out that you won't need a degree in accounting. In fact, it doesn't really matter. You have people who have no degrees, have done degrees in wide ranging subjects such as philosophy, medicine, French, history, etc., or people with poor grades but worked their way up through professional qualifications such as AAT.
Does anyone have any advice they can give me?
Decide which area of accounting you wish to go into. I primarily class them as:
There are further sub-specialisms, but it might be too early to look into them if you don't know what you specifically want to do. These can include: corporate finance, financial analyst, tax, consulting, audit.
Once you have found out which area of accounting that you want to work in, speak to accountants who work in the specific area that you want to work in and see if it's actually something you want to do. For most parts, you would quickly realise it's more about accurate reporting, and doing a lot of data entry quickly as opposed to using any maths.
If you are sure about the above, then I would recommend applying for an internship to see if it's actually something you want to do. I would recommend getting through the internship in one piece though.

Thanks, really comprehensive answer. My only thing with A-levels is that my A-levels are not high, although I have extenuating circumstances at the time (though up to the employer to decide if it's acceptable). I would hope that the GCSEs and BSc results make up for it, but if not would apprenticeships be the answer or would that overqualify me, and go the graduate route instead?
I've applied for PwC again, I did get to the interview stage a few years ago as they're lax with the A-level requirements. I think the other Big 4 firms have taken recent measures to do so too, however part of me thinks I won't have as much luck. Will probably give it a crack anyway.