I am from the United Kingdom, and although we originaly gave the world imperial measurements of feet and inches etc, we have used the metric system of mm for as long as i can remember - and i am in my forties.
Ah-ha! A callow youf!
So - my query.Obviously we have router manufacturers in the UK, such as Trend, but even they seem to make or at least advertise their cutters as either 1/2 or 1/4 inch although there are some refrences to collet sizes of 8mm and 12mm - which almost but not quite compare.
Phil will see more day to day usage in the UK and will probably comment, but my impression was, before escaping, that although people like Trend, Freud and CMT offer 8mm in their range, few users in the UK bought them and the 1/2" (12.7mm) and 1/4" (6.35mm) shank cutters were still the popular ones.
In short it's all historical. In longer terms the UK, Australia, etc and other parts of the former "British Empire" as well as the USA router shanks are commonly available in 1/4in and 1/2in (or 6.35mm and 12.7mm). Whilst I was taught in metric in the 1960s the engineering industry didn't make the switch until the 1970s and even there the change was never enforced in law unlike some countries - one reason why we quote distance in miles (and fuel consumption in mpg) whilst all fuel is dispensed in litres! Looking back we used to have routers with shank sizes of 3/8in (9.53mm) and 5/8in (15.9mm) although they've pretty much fallen by the wayside. In continental Europe thanks to a certain M. Boneparte they use the metric system with collets in 6mm, 8mm, 10mm and 12mm. Once again 10mm has all but disappeared in recent years although I think that Scheer still use it for some specialised cutters.
In reality in the UK you'll normally only see cutters with 1/4in or 1/2in shanks with a small number of 8mm shanks from specialised suppliers such as Festool, Leigh (dovetail jigs, etc) and the like. As Robert and Peter say 6mm is NOT 1/4in, 1/2in is NOT 12mm. In fact the only time you're ever likely to come across those shank sizes would be if you were to buy on somewhere like eBay Germany. I doubt that it will be an issue and if you wish to buy from the USA you won't have any problems as even the Americans use the same 1/4in as we do........ To be helpful most "European" router manufacturers (e.g. deWalt, Festool, Metabo, Felisatti, Freud, Bosch, et al
) produce collets to cover the full range of sizes both metric and inch. For example small deWalt routers (like the DW613 and DW621 and Trend T5) have 6mm, 1/4in and 8mm collets available in the UK whilst my personal favourite the DW625 together with its' siblings of DW624 and DW626 (and Trend T10/T11) have 6mm, 1/4in, 8mm, 12mm and 1/2in available. American manufacturers have traditionally not exported to Europe and therefore tend to offer only inch size collets (although Porter-Cable do list an 8mm collet for their routers) whilst the Japanese manufacturers seem to offer inch size collets in the UK but reserve the metric size ones for Europe.
The only problem area seems to be with low-cost (Chinese) imports where the people dealing with the tools sometimes can't seem to understand that 1/4in IS NOT 6mm and as a consequence they supply the wrong collets. A clear example of someone using an approximation as opposed to an absolute conversion of the sizes.
Hope that helps