Hi 'Geordie Daughter'. I worked for the Weights and Measures Department (later renamed Trading Standards) in the late sixties and covered the South Devon area roughly west of the Teign. This work involved visiting most trade premises on a regular basis. My only visits to any textile mills were at Buckfast and Buckfastleigh. The premises at Buckfast were adjacent to the Abbey and were quite large. There were many looms running in the sixties and the noise level inside was horrendous. The other premises were, as far as I can remember, were just of the main street in Buckfastleigh, but I have no memory as to what they were producing. One of the locations was certainly involved in fellmongering, that is the cleaning of the wool and the production of lanolin as a by-product.
There was an old mill like building at Harbertonford which at that time was the premises of an agricultural merchant. My thoughts were that it was an old grain mill, but I could have been wrong.
I worked the Paignton area in the early seventies and certainly never came across anything that looked like it might have once been textile mill. I would be very surprised to learn of there ever having been any textile mills in Paignton. I'm no expert, but they generally grew up adjacent to rivers as the trade uses a lot of water. Paignton is noticeably short of a suitable river.
I think the most likely option is that your loom tuner worked at Buckfast. OK, it's twelve miles from Paignton, but I don't think this would be too difficult a daily journey, even in 1939.