Have you thought about joining as an accountant? HMRC do employ accountants, there's one on my floor.
If you wanted to do the Tax Professional Development Programme (which is what I'm on), be quick, the closing date for next year's intake is next Friday for the online application - it's quite quick to do though.
The way the recruitment process works, they wouldn't know if you were a new graduate or not really - you start by doing a very short simple online form, which basically asks for personal details and confirmation that you have or are predicted at least a 2:2 degree, then you do a series of short tests about your working behaviours, maths, logical reasoning etc (think they take about 20 minutes each - they're timed). There is nowhere to say anything about past experience and you don't submit a CV, selection is based on the tests.
Next stage (last year - don't know if this year's process is the same as they seem to change it a lot) is a half day assessment centre, where you do another maths test and an in-tray exercise. However, apparently they do not mark the in-tray exercise until you are called for the final stage full day assessment centre so selection from there seems to be based on the test alone. Final stage is a full day assessment centre with written exercises, group exercises, a mock customer meeting etc. There's no interview.
So that is a long-winded way of saying that your age/past experience might be an advantage when it comes to doing the assessment centre and exercises, but you won't be asked about your past work either on the application or at any interview. My experience is that probably 2/3 of recruits have past careers. There are 7 of us in my office in this year's new intake, only one is a new graduate and 4 of us are over 30 (we've got one former accountant, too). I had expected most to have come direct from university, but new graduates are very much in the minority on the programme and ages are very varied - plenty of over 30's and a good number of over 40's.