for the record the carriage of transponders is a requirement within UK controlled airspace below FL100 when operating under IFR (but not VFR) with the capability for Mode A and Mode C with altitude reporting.
You should be able to select Mode C simultaneously with Mode A unless otherwise instructed by the ATS unit - whether this be for malfunction reasons or whatever
An exception exists for aircraft below FL100 in CAS receiving an approved crossing service.
OK so that's the legal, however I would suggest that most controllers would cope unless very busy and whilst not knowing if NM or NV have any local instructions, I reckon Chilli's right and you were just unlucky at Teeside
