I'm surprised that the CLX794 crew couldn't see the opposite direction, 1000' above traffic on their TCAS display, prior to making the request for higher. At cruising speeds/levels you would expect the TCAS to be set at a fairly long range. I know it's not the flight-crews primary duty to monitor the ATC situation from the cockpit, but on most of the post TCAS fam-flights I undertook, they did.
Had this happen several times:-
A/C Bigjet123 approaching level (......). standing by for higher.
ATC Bigjet123 roger, maintain FL(......), traffic crossing 1000ft above you right to left, x miles ahead.
A/C Yes we have that traffic on TCAS, or (even worse), traffic in sight.
I don't know whether this still happens in the UK.