Employers, by and large, literally do not care what subject your degree is in. They look to see if you have a degree, they look at your classification, and they maybe look where you got the degree. If you have a 1st from Oxbridge, it doesn't matter whether it's in underwater basket weaving or rocket surgery for generic grad schemes and roles.
It only matters if you want to go into a particular sector which requires you have particular skills beforehand - such as engineering, software development, the economic service, etc. In that case you may need either general skills from a smaller subset of degrees (e.g. a numerate degree) or specialist subject knowledge from a particular degree subject (e.g. economics for the economic service, engineering variously).
Even these can be ameliorated or subverted to some extent; there are an increasing number of software development grad schemes taking applicants from any degree, as they just teach you all the programming necessary in the scheme (and are instead looking for the people with the strongest transferable skills, leadership ability etc). For economics areas, you can do "conversion" diplomas/masters degrees. For STEM fields generally you can actually be funded for a second undergraduate degree in those areas if it's part time.
Additionally as noted above, even in those "specialist" areas, simply having the degree is not enough. It is essential to get appropriate experience from summer placements/internships, year in industry schemes, etc, and for software dev areas, to develop a portfolio of projects you've done on github. The times where a degree was sufficient to just walk into a graduate job are long since past - this only happens with medicine (and maybe dentistry) these days.
Unless you know you want to be an engineer, in which case obviously doing a degree in ancient history would be a poor choice, it really won't make a difference. Do a degree you have a genuine and sustained interest in, as that will be more likely to carry you through to getting a good result.