At some but not many. In Scotland it's more common, so you'd start with two or three (i think often related) subjects then drop one or more partway through. In England, many unis will let you take the odd module outside your main subject (often a language) but not necessarily have it formally part of your degree title. They might also run a few full courses with popular combinations of subjects, for example maths with philosophy or computing. Plus things like natural sciences or occasionally liberal arts.
Finally there's places like Keele, where more subject combinations are available and many students take them. In this case you either do both subjects all the way through (to come out with a dual honours degree, eg psychology AND neuroscience), or drop one after your second year so the second one gets named in your degree title as a minor (eg psychology WITH neuroscience). I can't think of other unis where this is common off the top of my head but I'm sure they are out there.
Hopefully that makes some sort of sense, given it's 3:30am lol.