If the OP has already booked, on a restricted I class fare there would be a EUR350 change fee plus EUR200 for the stopover in LON.

As this routing requires a transfer from either LCY or LHR to LGW, you won't be able to check bags all the way through anyway, so it would be possible to "miss" the final sector without any inconvenience to yourselves. I'm sure people miss connections like this all the time due to perfectly "normal" reasons like traffic, public transport, etc.

Not that I'm suggesting you break the rules, but previous posts suggest no problem, unless you make a habit of it.

Obviously, you won't get any miles or TPs for the unflown sector.