Newport has a sort of faded glory. What was fashionable some time ago, isn't now. The Hamptons of today just needs lots of money to penetrate: you can be a business-person, an actor, a chef, American, British...you just have to be able to afford a nice house there, and none of them are on the scale of the Newport Mansions. Depending on traffic, the Hamptons (which is a term encompassing villages and towns like East Hampton, South Hampton, Amagansett, Sag Harbor etc) can be anywhere between 3 and 5 hours' drive from midtown Manhattan. Newport is still, today, probably a 8-9 hour drive up the coast. There are regular private helicopter shuttles.
Martha's Vineyard (an island off of Cape Cod, which is a spit of land jutting into the Atlantic from the Boston region of Massachusettes) is arguably more exclusive than Newport. People don't value stone mansions with manicured gardens and staff quarters, as much as they value private beach access from a sprawling glass and wood house with stunning sunsets (which is difficult to reach). The Kennedy family was (is?) based in Hyannis, which is the mainland port (it's not really a port as such, just a large dock really) for shuttle boats to/from Hyannis and Nantucket / Martha's Vineyard (Nantucket is the island next to MV, it has a more conservative, preppy reputation and is for serious sailors). MV has a tiny airport, with lots of parking spots for private jets.
There's not really an equivalent of these places in the UK. I suppose you could say that Newport is a bit like Biarritz: its heyday definitely behind it, but still got good bones. The Hamptons are like very expensive and exclusive towns and villages dotted along the French Riviera, or the Amalfi coast. But that's not really accurate. It's difficult to compare.