Prime Minister Margaret Thatcher's opponents had a field day Friday after her deputy, Sir Geoffrey Howe, quit in protest of her resistance to Britain's integration into the European Community.

"Instead of having a leader who holds the party together . . . we have one who unfortunately allows the party to break up," said former prime minister Edward Heath, who himself was ousted by Thatcher as party leader in 1975.Publicly, key aides in Thatcher's 22-member Cabinet rallied round, although they take a more conciliatory policy than the prime minister in the drive toward European union.

Howe's resignation late Thursday prompted speculation that he or another senior lawmaker may try to oust her as leader of the Conservative Party - and thus the premiership - in a challenge this winter.

But many observers believe a leadership challenge would be too risky for the party, now less than two years from the June 1992 deadline for the next general election.

Howe, 63, a soft-spoken man who had come to irritate Thatcher profoundly, according to political insiders, handed his resignation to her without notice in a 30-minute interview on Thursday evening.

He cited "a growing difference" between them over Britain's role in Europe."We need to persuade friends as well as challenge opponents. We should be in the business, not of isolating ourselves unduly, but of offering positive alternatives," he said.

Thatcher responded that she did not believe their differences "are nearly so great as you suggest," and said she was saddened by his departure. Howe had stayed on as deputy prime minister after Thatcher removed him as foreign secretary against his will last year.

The end came for him when she lashed out after a European Community summit in Rome last weekend. The leaders agreed 11-1 to set a timetable for monetary union and debated proposals for closer political ties.

Thatcher shouted "No, No, No!" during a rowdy debate in the Commons on Tuesday and ducked an invitation to back Howe.

London's Financial Times reported Friday that Thatcher had berated Howe at Thursday's regular Cabinet meeting over his organization of parliamentary business.

Howe was the last survivor of the 21-member Cabinet named by Thatcher when she first won power in 1979. His departure left her government in apparent disarray and the prime minister increasingly embattled.

"Mrs. Thatcher may tower over her party as she towers over all she surveys," commented the pro-Thatcher London newspaper The Times. "But the tower is an ever-more lonely one."

Howe reverts to being a rank-and-file legislator, joining the ranks of senior dissidents. They include former Defense Secretary Michael Heseltine, the most popular choice, according to polls, to succeed Thatcher. He has also been obliquely criticizing her policy on Europe.

"The truth is that the problem is not a Cabinet minister here or a Cabinet minister there," said Paddy Ashdown, leader of the small Liberal Democratic Party. "The problem is the prime minister."

The split over Europe has blown up with the Thatcher government already in deep trouble. For 16 months it has lagged behind the Labor Party in poll ratings, and is now a daunting 16 points behind.