It's all very confusing - but it is all to do with fare codes rather than cabin codes that get printed on BPs.

Y generally means Economy J generally means Business Class. On UK Domestic these two fare codes BOTH mean Business UK - which is basically a Full Fare Economy ticket with lounge access.

On UK Dom "C" appears on the BP no matter what the fare code is whether it is Y,J,C,D,B H etc etc. on UK Domestic a Business UK fare is either booked using a Y or a J fare code (usually J but the Y is available from travel agents to scupper the attention of accounts departments who think it is business class). All other Domestic Fare codes C,D,B,H etc are NOT Business UK.

For European flights in Y - all Y fare codes Y,B,H,K etc will show M on the BP - same in World Traveller. For Club Europe J,C,D,R and I will show C on the BP whereas on long haul those same fare codes will show J on the BP.

Simples!