The OP does have a stopover in London, so a resonable chance that the OP wants to be in London and not at an airport
LCY is a great airport for arriving and departing from and has an easy journey to the London and Westminster cities
With 29 hours, no reason to change to LGW and , if holding status which affords lounge access, there would be no lounge access if booked on the BA codeshare to LGW