The Royal Army Service Corps (RASC) was a corps of the British Army responsible for land, coastal and lake transport, air despatch, barracks administration, the Army Fire Service, staffing headquarters' units, supply of food, water, fuel and domestic materials such as clothing, furniture and stationery and the supply of technical and military equipment. The T in the title of 17 Company indicates that it was a general Transport Company. During WW2 a standard transport company consisted of a workshop platoon, two or more transport platoons and a composite platoon. I imagine that 17 Company's post war (ie peacetime) establishment was at a slightly lower strength than its war equivalent. A transport platoon typically had about 30 trucks (still called lorries in those days) and each truck would be the responsibility of its driver, usually a private. Each platoon would be divided into 5 sections each commanded by a corporal. The trucks themselves might be
3 tonners,
6 tonners, or occasionally
10 tonners, or a mixture of all three. and would have been used for collecting stores from the ordnance depots and bringing them forward to the units in the formation (Division or Brigade) the company was supporting.
Having previously served in North Africa, by the end of the war 17 Company was based in Berlin. But by 1947-1948 when your grandad was serving, it was at
Wandsbek, a borough of Hamburg. Later in 1949 the company moved to Waynes Keep, near Nicosia in Cyprus and later still to Famagusta on the East coast of the island, so your grandad missed out on a sunshine posting!
The British Army of the Rhine occupied the whole of Northern Germany as shown in green on this map
but 17 Company would only have been responsible for supporting units in a relatively small area around Hamburg. As far as I am aware the area was the responsibility of the 1st Armoured Division, but whether 17 Coy was supporting the Division or one of its brigades is not known. Depending on the type of trucks in your grandad's platoon, he might have been employed ferrying cargos forward from the supply depots based down in the western part of the British Zone, using the larger 6 or 10 tonners or, doing more local trips driving a 3 tonner taking food, general supplies and fuel forward to the units. He would almost certainly have been making regular trips to places like Bremen and Hanover.