It's the airlines who pay for this service, I understand.
Not exactly. Someone else can probably give a better answer than me, but as I understand the money basically comes from a combination of:
1) Eurocontrol route charges - Anyone over 2MT flying IFR, 5.7MT flying VFR, and other criteria where charges are due
2) Navigation service charges - Anyone regardless of weight who is inbound and lands at the aerode providing the service (e.g. Farnborough)
3) Government funds - A small pot of money is allocated to incentivise units to provide a service. This money falls far short of the cost of providing the service.
Farnborough's job isn't necessarily to provide us with anti-collision information... It's to keep aircraft out of controlled airspace...
Though it would be incredibly silly to keep aircraft out of airspace when there is no chance of conflict.
Far better instead to be providing traffic information or deconfliction advice between actual aircraft to help pilots avoid collisions.
Unfortunately there will always be limitations of (radar) service provision when flying outside controlled airspace.
If someone wants a “guaranteed” service they should file and fly IFR inside controlled airspace instead.