With a PhD in particle physics, you'll get on most MSc programs in maths, and if you show expertise in a certain area of pure maths, lots of PhD advisors would be interested.
One thing I would say is that to convert from physics to pure maths really requires going from the beginning of undergraduate (at least via private study, which you'll find very enjoyable given your experience), so 4 years, then 4 more years or so for the PhD.
One fast track idea is Part III (MMath/MASt) at Cambridge (or something similar), but actually look at those exams. Eventually, you trace it all back to first year undergraduate courses you/I didn't do, like group theory or number theory. There is a lot of abstract algebra for example. There is no shortcut. The sort of maths you learn on a physics degree is of little value in pure maths (I converted to mathematical physics/applied maths career from a physics and philosophy degree). Pure maths is a world in its own, there is almost no crossover. Not so true the other way, but still very true.
You can skip straight to the PhD and avoid the previous degrees themselves, but you need to study this stuff, its amazingly different from physics. Once you know a certain area e.g. algebraic geometry to a graduate level (which requires 4 years of about part-time work even with a physics PhD, including more or less every course you see on a maths degree as a preliminary), you can definitely get on a PhD in that area. I suppose any attempt to fast track it will just make you passable but ultimately not particularly good at what can be an almost impossible research world to take part in even with 1st class honours etc in a maths degree. But not impossible, just need the desire and commitment.
Just teach yourself maths (i.e. all the usual courses, see e.g. here), then maybe do some research and publish it (you have experience in this). Then apply to do a PhD in that area, given you've already published in the field. That will probably be faster, easier and cheaper than the degrees, and you can select the courses directly that back up what you want to do. Getting a publication in a pure maths area should be a good sign you are very ready to do the PhD, as you know from your own experience in particle physics.
Could also be good to just apply now to some PhDs and see what happens. A crossover between pure mathematics and particle physics might be a good idea as you can sort of do all this on the job. If you self-fund it will be much easier, as the funding from what I understand is potentially reserved for first time PhD candidates. Much depends on the specific university/grant, though as I say they tend to bias funding for first time PhDs.