With picture-postcard villages, country pubs and an unmistakable air of affluence, there are few greater strongholds for Britain’s Conservative Party than Surrey, where voters have chosen Jeremy Hunt, the current chancellor of the Exchequer, as a lawmaker in five consecutive elections.

But even he admits that he may be out of Parliament after July 4.

“I’m very well known locally, I’m knocking on doors, I’m talking to people and I’ve got a certain following from my 19 years as a member of Parliament,” Mr. Hunt told The New York Times last week as he prepared to appeal for votes in Chiddingfold, 50 miles southwest of London. “But this is definitely the toughest it’s ever been.”

The fact that the second most powerful man in the government now sees himself as the underdog is testament to the scale of the threat facing the Conservatives at next month’s general election. Angry at economic stagnation, the impact of Brexit and a crisis in public services after years of government austerity, traditional Tory voters are deserting the party in the prosperous English districts that have long provided its most reliable support.

Several opinion polls predict a landslide victory for the opposition Labour Party that would sweep many longstanding Conservative lawmakers from Parliament. Although Mr. Hunt, who was raised in the area and still lives there, may yet beat the odds, analysts say he is vulnerable.

“I would be really surprised if Jeremy Hunt survives, frankly,” said Robert Ford, a professor of political science at the University of Manchester, adding that even if Mr. Hunt’s local connections, moderate politics and high profile won him a strong personal vote, “it’s not much of a life raft when you are facing a tsunami.”