LONDON, DEC. 16 -- So high is the discord these days over the state of Britain's National Health Service that eyebrows were raised over news that Deputy Prime Minister Lord Whitelaw, 69, who suffered a mild stroke Monday night, had been assigned a private room in a National Health Service hospital.

Whitelaw's affliction was unfortunate for the government in more ways than one. First, it coincided with the delivery to Prime Minister Margaret Thatcher yesterday of a petition signed by more than 1,000 NHS doctors protesting funding shortages that have led to elimination of 3,500 hospital beds.

Britain's state-owned hospitals were so overcrowded and understaffed, the doctors protested, that they were being forced to put male patients in female wards, and postpone operations to the point of hastening death in some cases.

More ominously for Thatcher, however, Whitelaw's incapacitation comes just as she was depending on him to help calm a rising revolt within her own Conservative Party over sensitive domestic issues such as health and welfare funding.

Having spent her first eight years in power curbing trade unions, selling off state-owned industries and building her international reputation, Thatcher has dedicated her third term to reforming the most basic ways in which Britons and their government relate to each other.

Weaning citizens from dependence on state-paid health care -- and making the health service work more for its money -- is just one of the crusades she has undertaken. Legislation has been introduced to fundamentally alter Britain's system of local taxation. Plans are well under way to turn the country's public school system on its head by allowing parents to take control from local authorities, and imposing standarized curricula and testing.

Some of the proposed changes are visionary, further steps on the long road to change Britain from an over-bureaucratized welfare state into a "Thatcherite" haven of free enterprise and individual self-sufficiency. Others appear to be more hardball political efforts to dismantle the remaining power base of the opposition Labor Party, which still runs local governments and school boards in Britain's big cities.

But the most significant opposition to Thatcher's reform plans has not come from Labor, still stunned from its disastrous third straight electoral loss last June. Much of the shouting so far has emanated from Thatcher's own long-acquiescent rank-and-file party members in Parliament.

On issue after issue since the new parliamentary session opened in October, Conservative members, while agreeing reforms are needed, have objected openly to what they see as extremism and unfairness in Thatcher's proposals.

The dissidents' numbers, up to 20 on some issues, still are small compared to the government's 102-seat majority in the House of Commons. But some senior Tories, including Whitelaw, are worried that the very fact of that massive majority, coupled with the weakness of the Labor opposition, could lead to the Conservatives tearing themselves apart.

"A government with a large majority is always in great trouble if it doesn't have a strong opposition," Whitelaw told a group of American correspondents here two weeks ago. Having strong opponents, he said, means "you can mobilize your own troops to fight. If not, there is a danger that your party splits up."

In the upper echelons of Thatcher's government, Whitelaw is the sole surviving representative of the traditionally dominant moderate bulk of the party that has been usurped by Thatcherite radicals.

His position within the government is considered inviolate. After losing the race against Thatcher for the party leadership in 1975, he became the Tory peacemaker, soothing feathers ruffled by the far right and reining in some of Thatcher's more extreme proposals.

As such, his role in pushing for the domestic reforms has been crucial, not only in the contentious House of Lords, where he serves as leader, but also in the Commons, where he sat for many years and retains considerable influence.

At the top of Thatcher's third-term agenda is the local government finance bill. It is designed to replace the current system of local funding through taxes on property owners with a flat-rate tax levied on all citizens over the age of 18.

Labor-led local governments consistently overspend, the government argues, because their constituents, primarily living in rental or government-owned housing, pay no local tax. Making them pay would relieve pressure on unfairly taxed property owners and indirectly persuade Labor voters to vote for more responsible government.

Opponents of the measure, including some former Thatcher ministers, call it a poll tax. Leading the opposition is a mild-mannered Tory, former environment minister George Young, who attributes his unease to a "gut feeling that what the government is planning is unfair." He is at the head of a revolt by at least 50 party legislators, by some estimates, who want the tax rate tied to income levels. They include John Biffen, whom Thatcher fired last summer as leader of the Commons; Michael Heseltine, who resigned as her defense secretary two years ago, and former Tory prime minister Edward Heath.

The proposed education bill has been even more vociferously attacked by Heath, and although he is often left howling alone in the woods in his frequent attacks on Thatcher, a number of senior Conservatives have expressed unease over the bill.

But the Tory malcontents, particularly those willing to speak out, still are a minority. Many of them look to the House of Lords, where the government does not have a majority, for effective opposition. While the House of Lords, composed of nobility who hold their seats for life, cannot kill a bill, it can delay and revise legislation in ways that amount to defeats for the government. It has performed that function with increasing regularity under Thatcher, thwarting her wishes on more than 100 occasions in the past eight years.

Thatcher repeatedly has pointed out that her government has spent more on the health service, at a far more rapid rate, than her Labor predecessors. She contends that the NHS professionals themselves are largely to blame for their problems, having grown greedy and inefficient at the government trough.

The NHS, directly funded by the government from tax revenues to the tune of nearly $30 billion this year, theoretically provides free health service at all levels to every citizen. But professionals insist that Thatcher's increases have not gone nearly far enough to resolve the health care problem.

Yesterday's petition by the doctors asked for an immediate infusion of another $380 million into the health service. When the government today announced an emergency injection of $180 million, Jill Knight, chairman of the Conservative legislators' health committee, said that it was "welcome, but I fear very much it won't be enough."