I have no doubt that it is not illegal to
continue (with ATC permission, etc) a flight in a plane whose equipment list doesn't meet the equipment carriage regs. To do otherwise would mean that if you are IFR in Class A and your ADF packs up, you would have to land in a field immediately.
But I would be concerned about
departing in such a case. The flight (if evidenced by an IFR flight plan for the appropriate IFR/CAS route) would be illegal to start with.
I don't think anybody has ever got done for this (despite widespread rumours about Cirrus pilots being done, etc) but that's probably because the CAA has bigger fish to fry, and also they would come out of any such trial (doing somebody for not carrying an ADF, which has no actual use in airways at FL150 anyway, and most other countries don't require it in their airspace) looking very silly.
It's the insurance I would be concerned about. Most loss adjusters are probably not savvy enough to know these silly little regs, and rarely go beyond checking the aircraft cert of airworthiness etc, but you never know.
But then I am not a lawyer, and if there is any case law on this subject it is being very carefully hidden
