LONDON - Mexican magnate Carlos Slim has taken a 3.16% stake in BT, Britain's biggest broadband and mobile operator, according to a stock market filing on Wednesday, in a boost to the company's new chief executive Allison Kirkby.

The stake bought by Slim, whose family controls telecommunications giant America Movil, has a market value of about 408 million pounds ($522 million), based on BT's closing share price on Wednesday.

Slim acquired the holding through his Inbursa financial company and two other group companies.

Shares in BT rose by more than 10% last month after Kirkby set out her ambition to more than double free cash flow over the next five years, cut more costs and potentially dispose of its global enterprise business.

A BT Group spokesperson said the company welcomed any investor who recognized the long-term value of its business.

"We have frequent communication with all of our shareholders and meet with major investors on a regular basis," the spokesperson said. "We look forward to engaging with Inbursa, just as we do with all investors."

($1 = 0.7816 pounds)

(Reporting by Paul Sandle; editing by Jonathan Oatis and Alistair Bell)