I never ever thought I would find mine, but I have!!!!!
I didn't know where exactly they came from, so it seemed hopeless, as all the expert advice says you must know exactly where they are from in order to proceed. I did know it was Hannover area, but that includes lots of villages.
After two years of digging around all over the place, the Lower Saxony Archives online gave me an Auswanderer (emigrant) record and the name of a village for one of the people I was pursuing. However, the curt response from the archivist to my query was that even if I insisted on pursuing this record when I wasn't sure it was mine, she would not be able to help me by sending it, at any price! However, in another stroke of luck, I found the Kirchenbuch (parish register) for that village online, in German, and I was able to construct a genealogy for that surname in that village, although I was not positive this emigrant was related to me.
Then, one of my other recently-discovered relatives posted all the info in a query on a German genealogy site, and, presto, we found our entire family. The person who responded had, for many years, wondered and talked with older relatives about what ever had happened to the 4 men who had left and gone to London in the late 19thC., who were still very much alive in memory. After having no contact for about 100 years, the family is becoming reunited, and my mum, well into her 80s but very well, finally has a second cousin, to whom she even bears a physical resemblance (she never had any second cousins before). Plus we have a history, and records going back to the 1500s! Our new relatives seem like very nice and forthcoming people; they instantly mailed us copies of a large number of documents. I have no doubt at all that we have the right family.
Never, ever give up! It can happen to you!!
Thanks to Rena and JustinL, who helped me out on this.