Er - I know this probably sound thick to you aviation types, but I thought the whole purpose of ATC was to look at the radar and then tell the pilots where to fly.
I would genuinely like to know how ATC functions without radar.
Its called Approach Procedural Control. The controller using separation standards based on time, distance, vertical separation and Nav aids, and in some cases deemed separations, Separate the aircraft.
NATS (apart from Aberdeen I believe) no longer use this as they have the staff and radar reliability (i.e mulitiple feeds to support)
You will find quite a few non-NATS airfields still using it Lydd, Manston, St Mary's, Cranfield, Oxford and Shoreham to name a few . Places such as Southend and Bournemouth and Blackpool will use it a night when Radar is not available.
Its considered a 'Black art' as less an less controllers rated to use it with equipment reliability improving.