In my personal experience, and through my network of friends/former colleagues, it's incredibly easy to find work as a contractor - in the UK at least.

I've never met a contractor who was short of contracts and options. There is pretty constant demand. Most of my contractor friends work 8-9 months of the year, take an extended break, then when they are ready for new work will land a new contract within 2-3 weeks at most. Totally normal to land a new contract within a few days.

Getting customers from abroad is tough in my experience as well. Have been doing contracting with a Swedish private limited company (AB) for soon ten years. Had many interviews for foreign companies, most within EU, but I have always fallen short, despite that it should be really easy to employ. Within Sweden, though, I have never had an interview that did not lead to an offer, so the national borders really matter in my view. To me, the reason(s) is/are unknown.