How do the grades of higher degrees equate with undergraduate qualifications, in terms of quality of work?
You state (emphasis mine):


  "I would very much like to know if the standard of work matches up to the same percentiles, in the UK. So, not how well someone is doing on the course, but if an undergraduate dissertation could be handed in and get
  the same mark on a Masters."


If this were possible surely the need for Master's degrees would not exist. Besides, don't you feel that the standard of your own work at Master's level is much higher than that at undergrad? I know mine certainly was. That's kind of the point. 

Say you need to get a 65 at undergrad to start a Master's degree, but you end up failing the course and getting zero. This doesn't nullify the 65 you already achieved in your undergraduate degree- but nor does it mean that you should have also got 65 in the Master's course.

The root of this answer is that you simply can't compare apples and oranges. Undergraduate and Master's degrees are designed to do completely different things, and just because one piece of work satisfies the requirements for an undergraduate degree does not mean it will satisfy the requirements for a Master's (and vice versa).