Do you have any flexibility to incorporate an overnight, or does this have to be done all on one day?
One option to consider if you can start your trip on Sunday 5th May:
Ticket 1
5 MAY BA1494 LHR-GLA 20:55 - 22:20
Ticket 2
6 MAY BA1481 GLA-LGW 07:35 - 09:10
6 MAY BA1480 LGW-GLA 11:10 - 12:45
Ticket 1
6 MAY BA1495 GLA-LHR 18:30 - 19:55
All legs in Club Europe. Ticket 1 is £302.29 and ticket 2 is £286.98 for a total of £589.27 (plus a hotel overnight near Glasgow Airport).