Oxbridge get 1s and 2:1s, whilst the 'lower' one in the Golden Triangle, ie KCL, would get 2:2s. But it doesn't mean anyone with that can get into it.
The thing about changing career path is that, it's difficult to enter a master's programme in those universities without a relevant degree. I mean, I did a BEd and I attempted to apply to Institute of Education, University of London for a particular master's programme which is in curriculum (ie not too relevant to my degree academically). The stated requirement was a 2:2 and they rejected me. The same institution, however, offered me to do another master's in a field relevant to my undergraduate degree.
I also tried to apply to University of Cambridge for a children's literature programme which obviously is not too relevant to my degree, but sort of a similar direction. They rejected me. Whilst at the same University of Oxford gave me an offer to do a master's in a degree highly relevant to my undergraduate degree.
Universities also don't just give out offers to everybody to get money. I applied to a programme at King's College London and they cancelled the programme after several months because of low application rate. Now, I don't think KCL would have problem getting 20 applications, would they?
And I don't come from some ex-poly either - my university has been the No 1 university in Asia-Pacific, and was No 8 globally in the field of education. We also have higher admission grades in general than Oxbridge for undergraduate studies.