At the time of the Industrial Revolution, the British were still measuring things in inches, pounds, etc. There was little trouble with machinery going back and forth- when the Robbins and Lawrence factory in Vermont made specialized milling machines for the British armory in Birmingham, England to make their Enfield rifles in the 1850's, they were in inches. And when the British in turn submitted one of their 1866 Snider Enfield rifles to the US for consideration as the new US breechloading rifle design, it was also in inches.

The UK discussed switching over the the metric system in the 19th century, but didn't until the 1960's. And full conversion didn't happen until they joined the European Economic Community in 1973- when they didn't have a choice.

I don't have a source on how the British dealt with European trade in machinery. For the imperial-measuring early machine shops, making things metric did involve another step: the change gears in the screw-cutting lathe might have to be swapped out, for example, to cut a metric pitch, and a different set of drills and taps used for threaded holes. And measuring tools would be metric or imperial, so a set of both would be required. But although the measurement systems might have been different, the tolerances would not be . A good mid-19th c. US or UK shop would be able to cut something .3937 inches in diameter, + - .0005 in. Whether it was called a centimeter or not was beside the point.