Of the major American watch makers in the late 19th and early 20th century, it seems that Walthams were the most common to be shipped to the UK, with in descending order of numbers - Elgins, then Hamiltons and then Illinois. The upshot of all that is that, these days, the most common US-made mechanical pocket watch to be found in auctions and on eBay over here is the Waltham in its various models. Elgins are less common but still plentiful when compared with Hamilton, Howard and Illinois.

I'm in the process of acquiring my second Bunn Special - should have it in a fortnight or so - in absolutely mint condition. It's a private sale. On UK eBay at this precise moment, there's not a single Illinois watch for sale! I check for them regularly and they rarely appear over here. Far more in the US - but customs duty and shipping made them very expensive to acquire...