No, there was not widespread support for the Western European SS units. The British legion was the least supported one. But the other legions from Belgium, and France did not have widespread support either. In two separate drafts only 1,700 French men joined the "Legion of Volunteers of France Against Bolshevism" , eventually to be joined by about 1,400 reinforcements after the unit suffered heavy casualties on the eastern front. Eventually, in 1943 Himmler ordered the unit to be amalgamated into the SS. In the Netherlands the initial draft only amounted to 2000 volunteers who were put into the SS Wiking division, by the end of the war around 12,000 Dutch men had served in the SS, one of the largest contributions to the Waffen-SS made by an outside country, though not all came from the Netherlands, as some came from the Flemish part of Belgium. The other major contribution to the SS came from Wallonia. Leon Degrell, a minor politician, joined the "Walloon Legion" as a private and eventually rose to become the commander of the Legion and it was transferred to the SS in 1943.

Now this may not be "British" but many of the Indian POWs captured by the Germans joined an Indian legion, that served in both the Wehermacht and the SS.

Source:

Hitler's Second Army: The Waffen-SS Edmund L Blandford