I have now spoken to someone who was involved with this, and he told me that they got Radway Green to make "about 100,000 cases" with this head-stamp so that they could make good quality ammunition for target shooters, as at that time a lot of the shooters were disappointed with the RG-made ammunition that had been sold to them in previous years (although RG had been trying to improve its "Green Spot" ammunition for some time, and had now introduced the new L42A1 sniper/target round with a 155-grain bullet, which shot well).
Tunnel Services used to advertise in the NRA Journals of that time (I can post a scan of one of their adverts if anyone is interested), their 155-grain "Palma" round being sold at £360 per thousand; their 144-grain "Radway Match" (with the "Green Spot" bullet) at £320 per thousand, and "Radway Standard" (with the ordinary 144-grain military bullet) at £290 per thousand. 36p per round for good quality ammo sounds cheap today!
This firm carried on loading target ammo until the mid-2000s apparently, and continued loading ammunition for Match Rifle until sometime later, before closing.
A correction: they did not have a tunnel range, the person who ran the firm had a house that was situated on top of a railway tunnel (that is apparently still in railway service), so that is why he adopted the name.
Roger.