Whenever Ive bought (or sold) a round (which admittedly is only a couple of times) Ive gone round with the previous cleaner and got them to introduce me.
Takes a bit of time, but the customers really appreciate it, they are a lot more comfortable meeting you before they see you up the ladder at their window. It also helps if the customer has any special requirements, its easy to point them out on-site rather than it being described and having to picture it in your head.
One customer I didnt manage to do that with came out as soon as I'd got the ladder up saying they had already got a cleaner, even though the previous chap had told them I would be doing the round. Had to explain I'd taken over, and I could tell she wasnt quite sure about it.