Hi, I am a direct descendent of George Finn and Ann Page. As far as I know, George was born in 1620 in Chilham Kent and Ann was born in 1621, also in Chilham. I have just come across the "connection" between George Finn and Sir Francis Fane also, and find it a large leap between aristocracy in one generation to the Finns in Chilham. Would be much easier to research if it is true. I have been able to find that Sir Francis had a son George....Col the hon George Fane...but he was married to a Dorothy, not Ann Page. It is a popular straw being clutched by many people as it seems, going by the number of matches I have found on My Heritage, but I really think it may be little more than wishful thinking.
Good luck with your searching.