Hi summer, sorry this thread had disappeared off my watch list as there were no new posts for a while.
I will try and answer all your questions in order...
"am assuming the training course has to be full time"
No, I am returning on 4 days a week - one day is in tutorials, one day is study at home and the other 2 days in the office. When I asked for part time hours they said 4 days was fine, it's possible to do less but you would have to discuss this with the course director. The exams and study are fixed and everyone in the country does them at the same time, but there is a facility to extend the 4 years to do the practical elements of the course (i.e. the job-based competency stuff that you do in the office) by two lots of 6 months. I hope not to need to extend, but basically once you're on the course then so long as you are passing the exams, they want to help you to get through to the end.
"I was thinking about doing some distance learning to improve my chances of getting an interview"
This isn't how the recruitment process works: there is no interview as such. There are various online tests followed by a one day assessment centre that comprises group exercises, a mock client meeting, written exercises etc. These are observed by assessors and scored and then those with the highest scores are offered jobs - with the highest scoring applicants getting first dibs on preferred locations. The online tests are about your work style, maths, logic/reasoning etc and I don't think you can prepare for them really, although you may be able to find practice tests somewhere.
"I was thinking that starting a part time degree in accounts and finance might be a good idea. From what you've seen so far do you think that would be worthwhile / is there something else that the time would be better spent studying? "
I wouldn't bother, personally - it won't help you to get the job. There are some accountants on the course and they get some very limited exemptions from some of the study, but not much really. I had no accounts background (you will have more than most of the other candidates simply by having done solicitors' accounts rules - which in my day covered a basic overview of how double entry book keeping works - that's more accounts knowledge than you need to be honest, you will be taught what is required from scratch, you're assumed to know zero about accounts and finance).
"Also how have you found attitudes to flexible working for those who are qualified? Would it be frowned upon not to work full time once qualified at least for a few years. "
I don't know to be honest as I am not close to the stage of applying for a qualified post - but generally part time working is very commonplace and accepted in HMRC. There are lots of grade 7 and grade 6 people working part time, many are partially retired. There are currently more jobs than there are people to fill them, plus the culture of HMRC is very flexible so I can't imagine it would be an issue to be part time. Nobody has suggested to me that I won't be able to stay on 4 days when I finish the course and move on to a grade 7 post. There are tons of different jobs available, not all of which involve work that is time critical or customer-facing, so there should be lots of part time options I hope!
I hope that helps a bit.