She was the eldest child of Admiral Nikolai Wolkoff (1870–1954) who was the last Imperial Russian naval attaché in London. Her family had decided to stay in Britain in the aftermath of the Bolshevik Revolution, and they became naturalised British subjects on 10 September 1935. In 1923 the Wolkoffs opened the Russian Tea Room, at 50 Harrington Road, South Kensington, near the Natural History Museum, a rendezvous point for other White Russians.
Anna and her father held right-wing, anti-Semitic views and were considered sympathizers of Nazi Germany, which she visited several times in the 1930s. She later claimed to have met Hans Frank and Rudolf Hess.
Her visits caused MI5 to take an interest in her activities and from 1935, she was placed under surveillance as a possible German spy. Wallis Simpson was a client of her couture business and also was under surveillance by British counterintelligence.
Wolkoff belonged to "one of many small anti-semitic associations in Britain", the Right Club, an antiwar movement with a membership of about 350, which had been founded by Captain Archibald Maule Ramsay, MP, who later stressed his patriotism in the House of Commons and said that there was a distinction between anti-Semitism and pro-Nazism.
Other members included William Joyce (briefly), who then defected to Germany as a broadcaster, A. K. Chesterton, later the author of The New Unhappy Lords, Francis Yeats-Brown, best-selling author of Bengal Lancer, Admiral Wilmot Nicholson and his wife, Christabel and the Duke of Wellington. The club's members often held their meetings in the Russian Tea Room.