At least ex-LHR and ex-YVR, BA and AC (and CP in the past) have run ApEx specials on business class fares (advance purchase requirements with minimum stay and change restrictions, etc.) from June to September. LHR-YVR has run GBP 1,400-1,500 r/t while YVR-LHR has run $3 (or possibly high $2ks). You could try a Flight Center near you to see if there are any.