I can second and third the suggestion that a BSA will make the trip without any big problems.
I've been doing it for years on mine. In 2005, my wife and I flew from Virginia USA to England and rode a friend's A10 1000 miles all over southern England. Much of that time we were loaded with 50 pounds of camping gear, which along with my 290 pounds and her 140 pounds, made a 480 pound payload (220 KG or 35 stone), and the bike never missed a beat. We (as you plan to) stayed mainly on the A and B roads and never went much over 55 MPH.
In 2006 here in the States, we loaded up a BSA A65 650, a BSA 441 single, and a 1955 M21 single, each hauling over 350 pounds, and rode 2000 miles around the eastern USA, visiting the BSA International Rally, the Ohio Valley BSA rally, Niagara Falls, and all points between. No problem with the bikes, rode on all sorts of roads.
Last year we were back in England, and my wife and I loaded 3 weeks worth of camping gear on a 1961 A10 (over 500 pounds/225 kg this time) and spent 18 days camping on the road in Yorkshire, Derbyshire, Cheshire, and the Isle of Man. Our only problem was that we found that the rear axle hadn't been assembled properly (there was an extra spacer in it that didn't belong) and we had to replace the axle bearings on the road. No big deal, we just stayed in the campsite another night while the part was delivered and put it in the next day. Motor and all ran just fine, about 1500 miles total.
So I wouldn't hesitate for a minute to head on out on your BSA, whatever type you decide to get!
Lannis