In general, as above, it's more of an advanced specialism so you're more likely to cover stuff relating to it towards the latter half of the course. I would note, in general, that the core subject for the area is control/systems engineering, which is normally covered in both mechanical and electronic engineering courses. However I'd suggest that an electronic background alongside the relevant control engineering options would be the stronger option in terms of industry - the mechanical side is somewhat more "pedestrian" and it's the electronic and electrical side which creates more challenges generally.
Regarding the degree courses available, various names are used but there are quite a number of courses that cover both the electronic and mechanical sides - electromechanical, mechatronic, robotics engineering and similar. Additionally some general engineering courses may cover both, either throughout the course or in the earlier stages. Per my above comments on the electronic side of things, a general engineering course which includes some core mechanics content in the earlier stages of the course, and then more advanced electronic and control systems theory in the latter stages would probably be the best option outside of a joint/combined course described above (which would likely allow you to tailor it towards one side or the other if you wished, or balance it between both throughout).
I would however highlight that the core area (control/systems engineering/theory) is very mathematical - it is an active area of research in mathematics departments as well as engineering departments. Bear this in mind in terms of your future plans and current background/preferences; robotics involves much more programming moderately complex mathematics than anything else. Styles of teaching this vary (my experience was it was done quite "un-rigorously", to my annoyance) however in terms of working in industry a stronger understanding of the underlying mathematics would be better than the alternative. Depending on your background you may want to consider an engineering foundation year, if you haven't had the chance to develop your maths to A-level or equivalent (this would also apply in general to engineering courses anywhere, but especially given your subject of interest and the fact that trying to develop more sophisticated mathematics on a looser foundation tends to be very challenging).
In terms of specific courses, I believe Southampton, Queen Mary (UL), Portsmouth, and UWE all have courses in the area I believe, which may be worth considering (and represent a fair range of entry criteria). Southampton also has an engineering foundation year, which may be appropriate depending on your mathematical background. I'm sure if you search any of the degree names mentioned above on UCAS you'll find many more options - do look at individual course content and what optional modules they offer in latter years of the course, as well as whether the course is accredited or not.