A few years ago, an American visiting London would have been hard-pressed to find a quality hamburger with a decent U.S. craft beer to accompany it. Now anyone can enjoy a Five Guys or Shake Shack burger in town, and then head to a pub serving Brooklyn Lager, in a sign the British capital is looking state-side for culinary inspiration.

Sandia Chang, the American founder of Bubbledogs, a hot dog and Champagne bar/restaurant in central London, said it is not just that London is becoming more American -- it's that the city's food and drinking culture is improving.

(Read More: Casual meets classy? London dishes up hot dogs …with Champagne)

"Four or five years ago, when I first came to England, it was still either a sit-down restaurant with tablecloths or a dirty kebab shop on the corner," Chang told CNBC. "The middle market was missing. There was nowhere where you could just pop up at the bar and move onto somewhere else."

But things are starting to change. Over the past few years, London has seen a boom in U.S.-inspired higher-end fast-food restaurants, with chains like Honest Burger and Byron opening a number of stores. Chang opened her London restaurant last year, and American fine burger chains Shake Shack and Five Guys opened their first U.K. stores in the capital earlier this month.

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The British are slowly becoming less traditional when it comes to dining out, Chang said. Rather than making a big deal of it, younger Brits pop into her restaurant, have a quick bite to eat, and then head on out.

John Eckbert, director of operations for Five Guys U.K., agreed that things have improved. "When I lived here 25 years ago, the food wasn't great, it wasn't well tended to and the customer service interface was pretty rough," he told CNBC.

(Read More: Bun Fight: US Burger Chains Do Battle in London)

He said the Americanization of London's food scene is just part of today's globalism, pointing out that Pret A Manger, a U.K. sandwich chain, and Nando's, a South African chicken-specialist, have both become big in the U.S. in recent years.

"The world's just a smaller place," Eckbert said. "Whereas it took McDonald's [to build] 5,000 units in the U.S. for them to then move abroad, that international cycle is coming faster than it was before."

It is not just an appetite for U.S.-style burgers that is growing. Brooklyn Lager's "brewmaster" Garrett Oliver said American brands are becoming increasingly popular abroad – especially when it comes to beers.

Brooklyn Lager is now sold across London, and Oliver said its sales had been helped by the New York borough's "cool" image, compared to its more upmarket and brash Manhattan counterpart.

"Over the past decade, the U.S. craft beer scene has become highly influential all around the world," he said. "It has partly to do with the rise of the IPA style and American hops, but also with the diversity and number of beers we have here."

And there is plenty more where that came from, according to Oliver. "We have more than 3,000 breweries [in the U.S.] and the number is climbing fast."