Well, in the end, at check-in in LCA, I was issued with a Malev BP for my onward flight BUD-SVO. The BP shows an SU flight number (not the Malev codeshare I had booked on) and my BA EC number.

The ladies at the lounge in BUD were very polite and asked me whether I had booked on the Malev codeshare. When I confirmed I had, and also showed them my BA EC card, there followed about 10 minutes of telephone calls, consultations of handbooks etc., but I was allowed in with a smile and an apology for the delay.