A masters degree in mathematical physics should generally be sufficient for most PhD programmes in particle physics, though depending on what focus you want to take it may be convenient for you to look for programmes that include some initial taught component to get you up to speed on anything they feel is required that you don't quite have yet.
A much more important component is a clear direction of what exactly it is that you want from a prospective PhD degree. If you can slim it down to a single research question, then that's a good fit for a direct pitch to a prospective supervisor, but if you can only narrow it down to "theoretical things" then it does sound like you should look for larger programmes that start off with a taught component and only require you to specialize after some additional exposure to the material.
Note, specifically, that the relative frequency and availability between these types of programmes can have strong variations from country to country.
As to whether your current qualifications are sufficient to make the bar for admission - that's for individual programmes to decide, and it will mostly depend on aspects of your CV that go far beyond just "a masters degree in mathematical physics". The only people who can give you realistic information are those admissions committees when presented with your full application package, including letters of recommendation - though it can be beneficial to make an initial informal inquiry with your CV (including transcripts of your BSc and MSc academic history) to a researcher close to the applications process, to see whether it's in the ballpark.
More importantly, however: for the type of detailed feedback that you're looking for, strangers-on-the-internet are not who you should be asking for help, as the answer depends too sensitively on the precise details of your situation. Our Q&A format is particularly bad for this, and while we can give you some more useful feedback on our chat room (once you have 20 rep), there's only so much that we can do for you. You need to discuss this in person with someone who knows both your situation and the types of particle physics that you're trying to get into.