I think Sweden is the closest example to follow, and any such switch would have to be done in the 1960s/1970s before the whole road system becomes too complex.
Bit of a double edged sword; switching would open up a load of nearby export markets for British car makers, but simultaneously open up the British market for them. I have no idea if the British car makers are up to the challenge of German efficiency or not.
Tariffs were far more important than anything else in keeping foreign cars out. Britain was the second largest car exporter and car producer in the world between 1946 and 1955 when they were overtaken by West Germany. This is most likely because British industry was in better shape than that of France and West Germany's. West Germany and later Japan quickly overtook Britain and by 1971 Britain's car exports had peaked and production would peak the following year.
Even before WWI, Britain's car industry was already showing signs of weakness. In 1913, around 1/2 half of the cars sold in the British Isles were Fords, assembled in Britain, however none were exported as Ford of Canada had gained the exclusive right to export Fords throughout the rest of the empire. Britain's ranked 5th in the world in terms of automobile exports, exporting just 1/2 of what the United States exported. France, however was #1 with 3.5 times as many exports as Britain.
Also telling before WWI was that 70% of British car exports going to the Empire with India, Australia, South Africa and New Zealand being the principal markets. Only 15% of British car exports were going to Europe (Russia being the largest single market, though even here the Germans sold 8 times as many vehicles). In the British dominions, the American marques were overtaking the British cars in Australia and were close behind in New Zealand and South Africa.
France in contrast sold 70% of their exports to Europe, Germany 75%. Both countries also exported more to Latin America was well. Even Italy, which only exported half as many cars as the British were gaining with 65% of their cars being sold in Europe.
Perhaps without WWI, Britain would have changed to right-hand drive as imported cars were relatively popular before the war. Britain had the world's second largest number of registered vehicles (behind the USA) even though it was only the third-largest producer. The post war tariffs insulated the British industry and the share of British-built cars rose.
Automobile Production 1913
USA 461,500
France 45,000
Great Britain 34,000
Germany 20,000
World War I delayed further expansion of the continental automobile industries and the Americans became the world's largest car producers and exporters, this gave the British automotive industry a few more years of life. With tax barriers going up, British cars remained somewhat protected in their home market along with the British Empire, where Canadian-built American cars tended to be the only competition. After WW2, the British government tried export as many cars as they could and for a while exports to the dominions and Canada were important, but even here the Germans and Japanese soon displaced them.
So simply butterfly away WWI and have French, America, German and Italian cars become popular. Without the war you won't have the high horse-power and petrol taxes come into fruition, giving larger and cheaper American cars more popularity in the British Isles.
