« Reply #1 on: Tuesday 03 September 19 01:37 BST (UK) »
Best advice I can give you is ignore the online trees. Use them as a starting point by all means, look at their sources (if any).
You say you've found a document linking John Gardiner to Elizabeth White. What is it, and is it an original document or a transcript?
Have you looked at wills for members of the Gardiner, White and Spencer families? Quite often a son-in-law gets a mention, or "kinsman".
I am Australian, from all the lands I come (my ancestors, at least!)
Pine/Pyne, Dowdeswell, Kempster, Sando/Sandoe/Sandow, Nancarrow, Hounslow, Youatt, Richardson, Jarmyn, Oxlade, Coad, Kelsey, Crampton, Lindner, Pittaway, and too many others to name.
Devon, Dorset, Gloucs, Cornwall, Warwickshire, Bucks, Oxfordshire, Wilts, Germany, Sweden, and of course London, to name a few.