Am I being overambitious with PhD applications
The requirements were listed as a 2.1 in an undergraduate degree, which I do not have (I got a 2.2)


You'll receive "desk rejects" from institutes that insist on this requirement. However, since


  I am currently studying for a relevant postgraduate masters and expect to get a good grade.


Your undergraduate degree might be ignored by some institutes, in favour of your postgraduate degree. 

Also, rather than approaching an institute, try approaching potential supervisors. They'll know how to navigate their institution's rules.

You should also consider whether a PhD is for you. You don't have the required grades. Perhaps something went wrong during your undergraduate degree; perhaps you'll achieve better grades during your postgraduate degree. This is perhaps something you've already thought about.