Unlimited flight pass is always the easiest if you are short of time but seems a bit of a waste, however TIME is valuable.
Seems one J ticket RT from UK might be in the right price range. I don't know current schedules from LHR but that used to be possible
e.g. LHR-YYC leaves LHR at 13:25 arrives YYC at 15:30 and YYC LHR leave YYC at 17:30 arrive LHR 9:20 (all in is less than 24 hours)

You could come to the Flyertalk DO if it worked into your plans in mid-November and stay one night, perhaps going back via YYZ?YYC-YYZ-LHR leave 8 arrive 6:30 or leave 12:35 arrive 10:10
PWNCF5 AC P Round-Trip 6038.00(CAD) Business SU / 12M 07 day advance (NEEDS P class)
allows outbound and inbound for a weekend trip if that is your preference.