It seems to me that
schlep is coming into fairly frequent use in Britain, MK.
Of course, "chiefly N. American" doesn't mean exclusively North American, but some British dictionaries don't have any geographical note for the word at all. Chambers labels it as slang, without any regional note, and MacMillan labels as American only the sense of a stupid person, but has no usage note at all for the other meanings including to carry something heavy and a long and difficult trip.
One of the earliest uses of the word in English writing was by James Joyce in
Ulysses (1922): "She trudges, schlepps, trains, drags . . . her load." This was quoted by language columnist William Safire in a 2007
New York Times article. I can't resist quoting a whole paragraph from Safire, because he casually uses another word that has recently been queried:
More recently, when world soccer's governing body issued a ukase banning play at high altitudes, The Washington Post began its coverage with this feature lede: "For most Americans, soccer is that game that forces parents to alter their weekend plans to schlep children, pairs of beat-up cleats and bags of soccer balls from field to muddy field."
The online index for
The Times and
Sunday Times, covering about a decade, has 207 instances of
schlep. Admittedly, this can't compete with the
NY Times, which has 428 hits in the past 12 months alone. Still, the word seems to be bandied about fairly freely in the UK paper. Most frequent user was Giles Coren, with 12 examples. "Bit of a schlep over to Chelsea, though." Looking at some other UK papers, the
Guardian and
Observer have 192 hits between 1999 and now, the
Telegraph has 71 since 2000, and the
Independent has "about 194", some dating from the 1990s.
Even a popular newspaper like the
Daily Mail uses the word: "Prep without the schlep: This kit will help with any pre-holiday revamps."
The word was even used in BBC Radio's
Goon Show: "Bloodnok: Thank you! Now then, I'll lay down and think of you as you schlep around looking for the old food there." ("The Childe Harolde Rewarde", script by Spike Milligan, 1958)
MK, you can't have been paying attention!
I'm not persuaded
schlep should be changed from common to rare.