Surprisingly, more likely than you might think.
Americans of German descent may be surprised to learn that thousands of Germans chose to immigrate to England and other British countries, rather than coming to America. Indeed, Germans were settling in Great Britain hundreds of years before there was even an America to colonize.
It was enough so that there is now even a genealogical society for Britains of German descent. The Anglo-German Family History Society was founded in 1987 and has close to 1,000 members, mostly in England, but also in other English-speaking countries.
http://www.agfhs.org/site/index.phpThe largest numbers of Germans to come to England occurred during the 1800s, and are due to a wide variety of reasons. There appears to be no single factor, or particularly significant time period, but rather a constant stream of immigrants, with typical ebbs and flows over time. Some key reasons included flight from political and religious persecution, over-population in some German localities, and economic opportunities in London, which was the main industrial center of the word.
And, don't forget that the English royal house was of direct German ancestry from King George I, the Elector of Hanover, in 1714 until Queen Victoria in 1837, and even she married a German, Albert of Saxe-Coburg-Gotha.
Source: Kory L. Meyerink, MLS, AG, FUGA