Bit of an odd question, but - does anyone know if a student with a 2.2 undegraduate degree and an MSc would be eligible for a BBSRC studentship if they wanted to do an MRes?

it's your Msc results that matter, not the 2.2. all the best.

You would qualify for a BBSRC PhD studentship, but I'm not sure if you'd get a grant to do a second masters degree. The 2.2 is important though - if you had a third and an MSc you wouldn't qualify for the PhD grant.