Did you keep it well watered. This summer has not been a good time for planting trees because of thehot, dry weather. Your tree would have needed several gallons per day.

Yes, the transplanting and warm weather will have stressed the plant. But, they are deciduous and as tough as old boots - don't worry it'll come back strong next year.
I cut a 10 foot specimen down in early August, dug it out having to chop through thick roots and planted it in my daughter's garden. It now has fantastic new growth!

Thank you and phew, what a relief I was thinking it was gone for good.
On the subject of being deciduous, will it hurt my new young Silver Birch if I allow the little caterpillars to eat the leaves?
I don't want to spray it because of the other insects [lovely green bush crickets] and because they are food for the birds.

Betula are tough - let the little wrigglers have their fill!
Birch and oak provide habitat and food for many species - and they haven't died out - yet!

more thanks - and another phew. I think [being a novice and planting lots of new stuff] perhaps I worry too much and am over protective. I have had a lot of trouble with foxes and squirrels digging things out so now guard them like a mother hen.

The birch will soon lose its leaves anyway, so I would not worry about the caterpillars.