This airspace was what is known as today as class G with a few exceptions such as Danger Areas. As such it is open to all. London Military did not 'control' it as such but would provide a radar service to anyone who requested it not just military traffic.
The type of service below FL245 would be Radar Advisory (roughly equivalent to 'De-confliction Service' nowadays) with Radar Control being applied to cross controlled airspace at place like Ottringham. Above FL245 it was Radar Contol.
Military Area Radar controllers are limited normally to a maximum of 4 aircraft, hence the frequencies would only sound busy when there was congestion and lots of traffic information and advisory avoiding action might be passed.