Most healthcare professions (very variable, the NHS has an entire website about all the different professions involved if you search for NHS careers), public services (teaching, social work, etc), engineering degrees are obviously associated with the engineering sector although it's not quite a directly linked as those others, law in much the same way (there are non-law grads in legal careers), public health officials, etc.
There are also more technical/specialist roles in many sectors e.g. oceanographers, ecologists, geologists, geophysicists, various lab scientists, software developers of various types, etc, which may require a more specific background although they may not be as specific about needing a particular accredited degree but rather a general background in a given field.
Really there are loads of different jobs and job titles out there, with varying required backgrounds. You just need to search around to find out more. There's a lot more out there than "lawyer/doctor/astronaut"!