Look at what you really want to do when you graduate.
Is a Master's essential? If it is, I'd do the integrated one. Not because your average will be better, but because you will be saving yourself over £4,000. Only do a separate Master's if you believe that the modules you'll take are essential for your chosen career path/serve your own intellectual curiosity but don't do it because you want a certain grade.
Most jobs and indeed universities recruiting Master's or PhD students only require a mid-high 2:1.
I'm someone who used to get upset if I didn't get a first in every single assignment, but it's not worth the stress.
When I applied to Oxford and Cambridge, I submitted my transcript from my first year of my first degree before I changed courses, on which there were 2 fails, both in the department that I was applying to.
However, I changed courses, did much better and graduated with a First and got into both Oxford and Cambridge and guess what - they only asked me to graduate with a 2:1 and didn't even specify high or low.
I know it can be incredibly hard and frustrating to get lower grades than what you're capable of, I totally get that. But it's not worth it stressing over it even more and going into more debt for just to get that 10% improvement.
Especially if you are not wanting to continue studying and you will be looking for a job, jobs would care even less if you got a first or not.