They don't seem to say anything about a requirement for a US-based card. You can apparently also pay via iTunes, and you can open a US iTunes account by buying iTunes gift cards in the US.
Location verification seems to be based on your Internet connection rather than your payment method, and you need to be able to connect from a location that is in one of the areas they cover.
However, if your goal is to sign up while you're over there, and then continue using the service back home, the FAQ says:
Can I watch YouTube TV while traveling?
YouTube TV works everywhere in the U.S., with live TV offered in areas where we’re launched. Your access to local networks will vary depending on which zip code you're in. Sign in from home at least once every 3 months to keep your account active. (Note, you’ll need to sign in from home monthly in order to stream MLB content.) You won’t be able to access any programs on YouTube TV, either live or recorded, while traveling internationally.
So, even if you are able to sign up, you won't be able to use the service once your back in the UK.