WHBM, very often I see on the search engines (Kayak, Skyscanner, Momondo) plus on airline websites themselves (BA in particular) connections from Scotland or Europe into one London airport but leaving from another. I remember you used to be able to through check your bags if you were transferring LHR-LGW, but it still wasn't very convenient. I have set up my own "connections" changing airports in London in the past, but being from the UK at least I expect it and am familiar enough with London.
Reminds me when I used to see many passengers missing their flights at PIK, having gotten in a taxi in Glasgow city centre and told the driver "Airport please", and been taken to GLA.