Thank you. I am amazed by hair raising stories without modern (or even adequate) navigational aids. Speeds reached 500 MPH long before the instruments were up to it. Point and hope, indeed; skill, more like!
Regarding civilian use, the answer is yes, but clearly not for long. In the BOAC Comet 4 Operations Technical Manual, DME pages dated 6 May 1960, the system is introduced as "Airborne Distance Measuring Equipment Mk.8B", and goes on to say, "On the omni-range aerials, ranges up to 200 nautical miles from Eureka Mk.7 beacons may be measured when the aircraft is at a minimum height of 28,000 feet."
This early DME system was by Murphy, who also developed and manufactured Eureka/Rebecca hardware. The DME control unit is in a smaller enclosure than a Rebecca Mk.8, but would have been immediately familiar to you, or any RAF pilot joining BOAC: the knobs are the same colour, marked the same way, with the same frequency letters and numbers, the same "omni/homing" switch, and so on. The range and heading indicator and distance flown gauge are identical to those used for Rebecca — same part numbers, too.
The trouble I have finding out about this now is that the system was short lived (at least in airliners), removed only a handful of years after installation, and forgotten about. Were Eureka channels listed in the RAF En Route Supplement, perhaps?
Guy.