If so, and if better seats are important to you, you should certainly consider flying via TLV/BEY/CAI. From TLV, the market to Cyprus is now far bigger and cheaper, with flights operated by CY (9 weekly), UP (low cost airline owned by LY) and IZ (flying both to PFO and LCA - however the routes are seasonal).

UP, for example, is currently charging $75 per way to LCA in December, and some of their flights depart 3 hours after BA165 arrives (usually that happens on Saturdays) so it may be convenient to you. CY also usually departs 1:30 hours or so after BA163 lands (however that may be too tight for a connection in TLV).

On the return (from LCA to LON) connecting via TLV can be much longer and less comfortable (the flight times usually don't match very well). However you can still book LHR-TLV//LCA-LON on BA, and just TLV-LCA on UP if convenient.