ROME, Sept 16 (Reuters) - The European Union's anti-smuggling and people trafficking operation denied on Friday that it had returned any migrant boats to Libya, after Britain's foreign secretary said it had turned back more than 200.

Boris Johnson said after meeting Italy's Foreign Minister Paolo Gentiloni in Florence on Thursday that the EU mission should turn back migrant boats as a deterrent and that it had "saved 200,000 migrants and turned back 240 boats."

The spokesman for EU's Sophia mission said no boats had been sent back.

"We have disposed of boats after rescuing migrants," Antonello De Renzis Sonnino said, suggesting there may have been some confusion.

Sophia's mission is to "disrupt the business model of human traffickers and smugglers," according to its website. But its ships have also made thousands of rescues.

It only operates in international waters, as the Libyan government has not allowed it to do so off the country's coast, something that might make it possible to send boats back.

EU vessels have pulled almost 26,000 migrants off overcrowded boats, almost 300 of which were subsequently destroyed so they could not be used again and to ensure they did not constitute a hazard for other vessels.

Italy is on the front line of Europe's migrant crisis, taking in more than 400,000 refugees over the past three years, many of them saved from rickety boats pushed out to sea by people smugglers based in North Africa, mainly in Libya. (Reporting by Steve Scherer; Editing by Robin Pomeroy)