I suppose if you want to go into consultancy, the knowledge that you pick up from a management degree would be useful, but it won't get you hired as a consultant. You can get graduates in something completely related like Literature going into consultancy. The general requirements for getting into consultancy requires next to nothing by law, but you are generally expected to be competent in the subject that you're consulting in and you need to be able to sell (people skills essentially).
For human resources, I suppose a management degree can give you exemptions for CIPD, but I generally don't consider the content in management degrees to contain that much about human resources. As CIPD Level 3 doesn't require any prior qualifications, you can more or less jump right in. The CIPD has 3 levels (3, 6, 7), and in total you shouldn't see yourself spending more than £19k to do all 3 levels (£6500 on the low end and if you shop around. see:
https://bradfield.co.uk/how-much-does-a-cipd-qualification-cost), if you ever had to pay for all of them yourself. If for some odd reason you need to do a master's related to HR, you usually don't need a specific undergrad in the subject to do it (to my understanding). You also need next to nothing to get into the sector by law, and graduates who do enter the field usually come from a whole variety of backgrounds (like consultancy). You will often get training in the field as a new entrant.
I don't know much about the employment of product managers, so I can't really give a fair assessment of this area. Having said that, the following link suggests that you don't really need a specific degree to do the job:
https://nationalcareers.service.gov.uk/job-profiles/production-manager-manufacturing-As with most jobs, employers usually care more about relevant experience more than anything.
I tend to focus on degrees that are specifically required for jobs (by law ideally) and that you can't get around this requirement without going to university e.g. you can become an accountant, programmer, solicitor, finance professional, writer, and performer without going to university, which can render the point of getting a degree for the sake of these jobs rendundant; however, you cannot get around doing a degree for a career in nursing, vetinary science, dentistry, or teaching, for example.