根据女士说的时间Since the 1940s，my great grandparents came here during the war，可推测她的家人是 在二战期间迁居到英国的。

【听力原文】
M: How long has your family been in England, Nadia?
W: Over ages. Since the 1940s, my great grandparents came here during the war. I' ve lived here all my life.
M: Have you still got relatives in Germany?
W: Yes, we have. We went to visit them about ten years ago. We haven' t seen them for a long time now, but we keep in touch by e-mail.