It is nice to know a like- minded neighbor, as the resident of No. 10 Downing Street, Mrs. Thatcher, does. At No. 11 resides, because she put him there, Nigel Lawson, chancellor of the exchequer. He is, physically and spiritually, one of her stout supporters. The barrel-chested Lawson moves into a room or an argument like a tank well- fueled with certitude.

Here, as across the Atlantic, a conservative administration has found government harder to shrink than it had supposed. In Britain, Lawson says, there is, for example, a close connection between the construction industry and conservative MPs. Parsimony does not extend to public works. In Britain, too, public works have been ennobled with the title "infrastructure," the better to enable conservatives to look out for "our people."

The Thatcher experiment, like the Reagan experiment that began 18 months later, has cut the rate of growth of government. But Thatcher has a problem Reagan no longer has, and Reagan has a problem Thatcher decided not to have.

Thatcher's problem is high unemployment -- 13.4 percent and rising in the fourth year of a recovery. Actually, the rate may be 16 percent, counting those who are "employed," but should not be, in overmanned industries and public agencies. But, then, Lawson says, some of the 13.4 percent were virtually unemployed five years ago, when they were on public and private payrolls.

Besides, no one knows how to stimulate the economy and sop up unemployment without re-igniting inflation. Furthermore, Thatcherite doctrine is that government has a larger obligation to cure inflation than unemployment because government causes inflation. This violates government's promise, implied in the issuance of currency, to maintain the currency as a store of value.

Thatcherites say they would be doing better were it not for the continuing costs of the Falklands and the miners' strike. Such complaints against the vicissitudes of national life really should not issue from a government floating on North Sea oil. However, some of Britain's unemployment is a sign of success. Because of sharply increased productivity -- a result, in part, of putting the economy through a wringer of recession -- there is steady growth produced by fewer producers.

Economically and politically, Lawson says, Britain can get along adequately with double-digit unemployment. Economically, he may be right. But the social costs could change the political equation.

An intriguing difference between the Thatcher and Reagan approaches is that Thatcher decided, early in her first term, to act boldly to shrink the PSBR -- the "public-sector borrowing requirement." (That phrase is superior to, because it is more descriptive than, the word "deficit.") So, in 1981, even though Britain was in a recession, the government submitted the most unpopular budget in decades, raising taxes substantially.

The theory was that this would prevent government borrowing from "crowding out" private borrowing needed for investment. This, in turn, would lower interest rates, suppress inflationary expectations and spur growth. Instantly, 364 economists signed a letter to the London Times announcing, with characteristic finality and inaccuracy, that it would not work. It did.

Today, the government led by the Downing Street neighbors is an interested, not to say mesmerized, bystander as the Reagan administration contemplates its deficit. The U.S. economy still is the locomotive that pulls European economies. And the high U.S. interest rate (which reduces the sting of the deficit by pulling in foreign capital to help finance it) siphons capital away from European investment.

The Thatcher government now has tax-cutting plans. It thinks it has earned them by doing unpleasant first things first. Taxophobes in and around Reagan's administration say that when the economy is growing, one need not raise taxes, and when it is slowing one dare not. Lawson's narrative refutes this. He is too discreet to intrude upon U.S. arguments, but too intelligent not to know the lesson his tale teaches.

For Reaganites determined to attack the deficit only with spending cuts, there recently was an instructive event here -- a middle-class riot. The Thatcher government announced a plan to reduce education subsidies, thereby requiring middle-class parents to pay significantly more of the costs of university educations. So 8,000 students took to the streets and bridges of central London at rush hour. There were 180 arrests.

As one student said, indignation mixing with incredulity: "They're cutting our standard of living!" Conservative back- benchers, hearing howls from "our people," confronted Thatcher with the most serious rebellion of her five years as prime minister. As Reagan will soon see, hell hath no fury like that of the middle class when its subsidies are at issue.