This past year I worked with a couple and their two lovely little girls also from the the UK, found them a rental house in Bronxville, and they are currently looking in the same village for a home purchase. ALL this was done long distance except for final walk-through and lease signing. They would be able to give you an honest opinion of the process.
I look forward to hearing from you and giving you the contact info for that client.
Bob Granata 914 668-9514
If you need help locating suitable local properties for purchase...AskRey.
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Rey Hollingsworth Falu
Licensed Associate Real Estate Broker
Houlihan Lawrence - Bronxville