Make no assumptions with insurance- read and understand the policy before money changes hands. Never let your broker change your anything without obtaining your express permission first- and get that in writing. Unless the policy clearly says you're covered, then you're not covered- insurance is a business of written specifics.
Can't say for anywhere else, but in the US you can get a "Personal Liability" policy that covers anything you do anywhere within it's coverage area, and it generally has no limitations concerning where you are, just that you are there personally. It takes effect after any other insurance coverage is exhausted or where there is no other insurance coverage. About the only thing it doesn't cover is intentional malicious criminal acts. If you have assets which you don't want to risk or you do things beyond what the average person does, then you need such a policy. The cost is tied to the coverage and coverage usually starts in the million dollar range and goes up. It ain't cheap but unless you're set up with protected assets, then you need it- if it pays off once it will be worth it.
Disclaimer: I have nothing to do with any insurance companies; in fact I hate paying it myself but it's a necessary evil in life so....