Henry Charles CO Kind Regards Trevor Ellissier French Ancestors

I recently posted a small family tree of Henry Charles Cosier and Emma Banks. He was born around 1825 at Hackney. A familiar story told to me when I was growing up is that the Cosiers fled France at the time of the Hugenout prosecutions 1650-1700 and went to London where they opened a business, eventually coming to New Zealand and then Australia (Henry Charles Cosier and Emma Banks). This story was told to a cousin by another relative.

So, can anyone suggest how they came to London and how I can find the details?