Over 18, American girl needs some dating advice with a British Gent.?

I like a British guy. We met on vacation here and stayed in touch. How do I move the friendship to the next level. I think he is interested but the calls and contact haven't moved ped 1x every week or two. He works a lot and is older and set in his own ways. He is a shy and reserved British man and not sure what to expect. Calls last 1 or 2 hours (although calls are recent since we started out emailing). Any British dating insight would be helpful. He's in the UK and I'm in the US.