I would note, Chemical Engineering and Biological Engineering are not "Engineering and Chemistry" nor "Engineering and Biology". They are specific fields of their own, and are actually somewhat different to most other engineering disciplines at that.
While I knew of the Bristol course above linked above, the L'boro one is news to me but maybe unsurprising given their emphases in subject areas - both are also very good universities generally for those STEM areas so neither is a bad option. Generally though "Engineering Physics" exists but is more of a US thing than a UK one. If you are interested in both Engineering and Physics, there are some other routes than an Engineering Physics degree however:
As indicated above, you can start Physics undergrad course then an engineering masters (or PhD - many of my EE lecturers were originally Physicists) - there are a few "conversion" type masters which also satisfy the academic requirements of the CEng without further qualification (otherwise you would probably satisfy them but might need to submit some documentation confirming you've met those requirements between your physics and engineering backgrounds). You could also take some relevant modules as optional modules along the way to getting your Physics degree - it wasn't that uncommon to occasionally get Physics students taking Solid Mechanics or one of the electronics modules at Exeter when I was there. If you aren't so concerned about time frame, then you could get first (i.e. undergraduate) degrees in each area. Currently, SFE provides funding for part time second degrees in STEM fields - this includes many engineering and related courses. It might also include Physics, although the only Physics degree that is routinely offered as part time as opposed to in an ad hoc fashion is at the OU to my knowledge.
You can do a first degree in engineering and then go into Physics, however this more or less restricts you to Electronic/Electrical Engineering or Materials Science/Engineering degrees for the first degree, as those are the only engineering disciplines routinely accepted for Physics masters (UCL and Imperial both specifically note EE is acceptable for their Physics MSc courses). Alternately you could also do a first degree in Engineering and take some optional modules in Physics in the course of getting that degree - however there are issues with prerequisites, timetabling, whether the Physics department will accept that, and also in the fact that often optional modules are heavily limited on engineering courses due to core module requirements, and due to accreditation purposes you can often only take one or two such modules "external" to your main department or engineering more broadly.
Alternatively you could also do Maths, which in an appropriate course offering a range of applied mathematics and/or theoretical physics options if often a suitable background to go into either and/or both. You could do an undergraduate course in Maths, taking the AM/TP options where applicable/possible (although there are plenty of purer options in analysis that would be very relevant, or maybe Lie groups on the algebra side), then a masters in say Physics and a PhD in Engineering. There are also many more options for joint courses between Maths and either Engineering or Physics, which would often suffice to go into the third area (perhaps even better than just doing one of the two latter subjects), compared to between Physics and Engineering. That said, if you aren't keen on Maths and balk at the prospect of having to write a proof for any of the calculus and differential equations you'd be using to solve problems in engineering/physics contexts, it's probably not a great idea.
I would note as far as working in the engineering sector is concerned, you needn't necessarily have an engineering degree - some roles may require it, and some sectors may be more likely to need it than others, but there are quite a few roles where a general numerate, physical sciences background would be sufficient to start off with. In terms of doing engineering work on particle accelerators, this does happen but bear in mind there aren't exactly a lot of those so inevitably it's not something you're going to specialise in at the undergraduate level, or even at masters level - maybe in a PhD project. However you don't need a PhD to work at e.g. CERN in their engineering areas. Typically an EE degree would be the most relevant background, although a general engineering course or a mechanical/aerospace course with a reasonable amount of electronics coverage might be suitable (although I think you would really need that plus the EM wave/field content more typical from an EE course or a Physics degree)...materials backgrounds may also lend themselves to some elements of particle accelerator engineering, but this is likely on the research side of things.