I’d say that in your position, the masters you do will be more of a means to an end, so you can get to the PhD/DPhil stage and be able to focus on the particular area that interests you. For that reason, an LLM which gives you as much latitude as possible to select criminal and public law modules is probably your best bet (LSE?). Personally I would not recommend a criminology-type masters - it’s fundamentally a different specialism.
One thing I would add. There are obviously plenty of criminal law academics out there. But many will have spent time getting some form of practical experience, even if it isn’t at the bar/as a solicitor. For example, lots will do judicial shadowing, or work for the Law Commission, etc. I suspect the reason for that is that crime is an area of law where you really benefit from a bit of hands-on experience in the criminal justice system, or at least being around people who have, even if only for a short while. I expect it is quite challenging to make any meaningful contribution to criminal law academia if you’ve never set foot inside a courtroom or watched a criminal trial from start to finish. So although you have ruled out practising as a lawyer (which is of course completely fine), do bear that in mind.