As a Canadian, we have the equivalent of the NHS, so even as a young guy in my 20s going to the States, I always got a robust, known daily travel insurance for being in the states.
My parents always drilled into me the importance of this, as even the smallest of hospital visit for a fall, broken bone, x-ray, cast would be multi thousand of dollars or pounds. Any serious injury and hospital stay is getting into tens of thousands and hundreds of thousands.
Serious life changing financial burden potential.
Very scary stuff, so do use an established travel health insurance.
For a cycle trip, I'd recommend asking over at the UK bike forum, the CTC one, for current cycling touring specific travel insurance.