But the paid upgrade is only one-way; we just booked CLT-LGW for about $700 pp all-in. Plus you have the luxury departure tax which is either £60 or £120, I forget which, but either way it's not pocket change.

If the OP posts travel dates I'm sure someone can look at the loads; last time I went on this route it was quite empty and my sister and I took over the middle section of 4 seats with no problem. The OP may be flying when the plane is empty enough to pick a window/aisle combo near the back and be flying next to an empty seat.

If the OP has any US miles then the miles + money upgrade to Envoy is another idea. 60k miles round trip plus $600 plus the departure tax so it's more inline with the out-of-pocket expense of second seat ticket (although second seat doesn't require the miles to ve spent) and it's guaranteed in advance instead of at the gate or at check-in. There seems to be good availability on most of the dates I checked, probably because J pax (paid, miles and cp certs) are flying PHL-LHR for the Envoy Suites.