Edit: read up on it a bit more and as I read it, both are accepted, and one only appeared about 10 years (documented version as always in these cases, you are never sure when things Actually were used in speech, only when they first appear in written sources) after the other. So nearly simultaneously, or better yet got altered from early on.
this is what I found in 30 seconds (first 2 hits): "Up the garden is used more frequently in the United Kingdom, while down the path is used more frequently in the United States. But both are correct." So not just UK.
The first known published occurrence of 'lead you up the garden' is in Ethel Mannin's 'Sounding Brass' (1926)
There is another quote from 1925, this one from minutes of a meeting:
"I shall try very carefully not to follow the Chairmans's lead this morning. He was leading me up the garden a little"
– it is from Commission on Food Prices: First Report, with Minutes of Evidence and Appendices, H.M.S.O., 1925
and:Hansard has a number of early references, such as this one, 1926:
'if I may use a vulgarism, he is trying to lead his supporters "up the garden." link