Audiences in London are different. They'll fall all over a big Hollywood star just like us Americans, but they'll also spend top dollar to see a new play starring stage actors if it's supposed to be good. You could hardly say the same for Broadway. There are only one or two straight plays per year not starring TV or movie people.
The costs of putting on a show are lower as well. A show doesn't have to play as long to earn money. The market is less driven by awards, so there's less pressure to stuff a bunch of openings into one month like every April in New York. There are also, as has been pointed out above, more venues. Those venues need shows, and not everything is meant to run forever.
One thing I am consistently surprised by is how short the turnover is between shows. I am not sure about how London unions work, but well respected non-profits like the Donmar Warehouse or the Old Vic can close one production, tear down the set, load another set in, tech the show, and open for previews in less than two weeks. That'd never happen at the Atlantic or Second Stage.