In terms of the solicitor route- I know this sounds a bit counter-intuitive but I think there is a danger of becoming over-qualified. A masters is acceptable, but I wouldn't take it any further than that, otherwise firms will tend to think that you're a wishy washy academic with no interest in the practical side of the law.
Obviously the Bar is a bit different and generally academic prowess is very much treasured. However, I still think care has to be taken when making sweeping comments. The Bar is not a monolithic block. If you want to be a chancery/commercial barrister (i.e. someone who deals with big contractual disputes/company disputes/offshore trusts- it's a very broad practice area but that's the typical type of work) then I think you will have severe difficulties even getting an interview. The situation could perhaps be rectified if you did something like the Oxford BCL, the Cambridge LLM or the Harvard LLM as a post-grad degree. Clearly you would need a first to do that, and then you just hope that one of them lets you in! It sounds like you are on course for one though, so hopefully you will put yourself into the best possible position.
However, at a criminal chambers or the CPS, or even a mixed criminal and civil, the odds are slightly higher. I'm by no means saying you would be guaranteed pupillage, because it's still tough, but I still think that a first, even from a mid-tier university, may be looked upon favourably.
The bottom line is that you need to do the research on the types of areas that, with your CV, you could realistically practice in. It will be a hard road ahead, and you will probably experience a lot of rejection (something I am starting to get used to myself) as you go on the quest for that elusive pupillage. However, if you are really determined and focused there is no reason why you shouldn't give yourself a fighting chance.