LONDON — After decades of delay, the British government endorsed the expansion of London’s Heathrow Airport on Tuesday. The decision to build a third runway at the airport provoked a ferocious response that illustrated why a succession of politicians have ducked the issue since the 1970s.

The announcement was meant to end years of political paralysis over aviation planning in southeast England, where Heathrow is now operating at 98 percent of its capacity, causing Britain to lose ground to airline hubs on the European Continent.

But the decision announced on Tuesday by Chris Grayling, the transport secretary, is just the start of a lengthy process that is sure to face legal challenges. It also presents Theresa May, the new prime minister who has opposed a Heathrow expansion in the past, with a crucial political test.

The government has bought some time by delaying a parliamentary vote on the matter until next year. Two of Mrs. May’s cabinet ministers — Justine Greening, the education secretary, and Boris Johnson, the foreign secretary — oppose the project; Mr. Johnson called it “undeliverable.”