Thanks for the replies from Gary and Eegore, which were helpful. No, the poor running on start up and for first five miles or so is not just because the engine is cold. I have been riding bikes since the early 1970s, and plenty of bikes with carburettors and chokes, so know how a bike should run and when it's not quite right.
Yes, the problem is almost certainly running too lean and a re-jetting is needed, and I am taking it into a really fantastic bike mechanic locally on 16th September who is going to look at re-jetting it.
Yes, the original problem for which it went back to the dealer twice was very serious bad-firing and silencer that was too loud because the previous U.S. owner had taken the baffles out.
I did not pay the dealer anything extra for when it went back to them and they picked it up for free (twice) and took it back to the other side of the Pennines (and in fact it's still under their 3 month warranty). They DID rebuild the cylinder head and replace the exhaust valve liners, etc., as described. They've tried twice to sort it out, and so there is not much point in sending back to them again, so I'm trying my local bloke for the re-jetting.
Meanwhil I am buying a brand new Royal Enfield Meteor - had a test ride on one - they are terrific bikes, refined 2021 engineering.
Thanks for your help, guys.