An Annexe 6 transfer may prove to be your salvation. This allows an airline to operate a foreign registered aircraft on its own AOC. However you will need the co-operation of the Owner of the aircraft, the lessee and or lessor, the airwothiness Authority of the contry of operation and finally the CAA. Having said all of this, if your aircraft type is only approved for operation inn the Private Cat., the I can't see CAA allowing Public cat ops in another country whilst still on the G reg.
Good luck.