IFR certified a/c - required on C of A?

[High Wing Drifter]

If a plane has non-FM immune radios does that mean that it can't fly IFR in controlled airspace?

For Comms and less than 5700kg (I think), no. For VOR, as flight in CAS mandates those for carriage, then they must be FM Immune. immune ILS is reqiured for ILS approaches.

Best check for your self: Airworthiness Notice 84 on the CAA site.