I live in the UK (Liverpool) and I would suggest that if you want to end up with a Doctorate (PhD) in theoretical physics you must study for a BSc (Hons) in Physics first. I worked at the Liverpool Uni most of my life and I can say that, as far as I know, you can only study for a doctorate in the UK if you get a, " first" in Physics. If you don't get a "first", but get a 2:1 or even lower a 2:2, then you need to do some more intermediate study like an MSc before being allowed to do continue to do a doctorate. We had one guy come over from the USA and he said that getting a doctorate in the UK was a "doddle" (much easier) that doing one in the states ; although, I know many here will disagree with that! He claimed that in addition to his research work they were expected to take and pass several exams too. Basically, you are supervised by a supervisor and you have to come up with a topic of study. The topic has to be a unique one that adds to science knowledge base and not simply a repeat of someone else work. Normally, studying for a doctorate takes 3 years but in can also take 4 years or even longer if you come up against some problems like someone else has, " stolen your thunder". Any good supervisor will enable you to diversify your material so that there is enough new material to enable the new work to be accredited. At the end is a viva where you are asked to explain your work and answer questions from a group of three experts (one of whom is your supervisor) in the specific topic in the field that you have chosen. They will have read your work and checked your results graphs and data in the months before the viva and will give you the result on the day. Normally, if you pass, there will be spelling mistakes that have been spotted; graphs not properly referenced within the text etc that you will need to do. You do not officially have the title of Dr status until the award ceremony (at Liverpool twice a year). Clearly, mathematics is pillar of support when studying physics at degree or at a higher level. But make no mistake, you will be put yourself at a serious disadvantage in studying theoretical physics if you have not mastered the basics at BSc level and BSc (Hons) at best. Mathematics while very useful will not carry you very far unless you have understood the basic principles in Physics at degree level first.
It's been my experience that some supervisors are better than others; you will be wise to speak to current PhD students and get their opinion of whom they consider the best and most helpful. The supervisor can guide you but he/she can't do the work for you.
Normally, the reason the high calbre students are selected is because they are often financed in there studies by companies who have a vested interest the particular area of research. Research grants are awarded too. It is also possible to fund your own way through to a PhD and maybe the entry requirements and research topics are not so restricted.