No, that’s not true about the NHS reimbursing costs - I’ve never heard that before and I’ve been visiting the US (and taking out travel insurance for it) for over 20 years.
I would shop around some different travel insurance companies and see what prices you get. You will need to make sure you select policies that INCLUDE USA and Canada, as you need to make sure you have enough medical coverage for the US healthcare system (£10 million is usually recommended).
You’ll also need to check whether the policy covers anyone resident in the U.K. or if you need to hold ILR or citizenship to qualify
In the past, I’ve bought my travel insurance from (I’m a U.K. citizen):
Boots
Endsleigh
STA Travel
Debenhams
And you could also try places like:
M&S
Post Office
Tesco
And maybe look at Go Compare or Money Supermarket for comparisons.
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