They were all a very much on-off-on-off service through the war, apart from first class in the London area, which went in 1940, never to return. Someone will have the details. It likely varied dependent on who the civil servant was in charge of the relevant department at the Ministry of War Transport.
Amusing account from mid-war low times on the GWR, a few restaurant cars were still running despite shortages of, locomotives, staff and food. A departure from Paddington was stuck there waiting for a loco to be found. Meanwhile the restaurant car served the first sitting, relaid, served the second, relaid, they were still stuck there, a third was announced and they duly all filed in. No menus, you just got what there was. The wizened elderly GWR chief steward took up position mid-car. "Saute of whalemeat, gentlemen", he announced ...