The question in British politics is not whether the ''Iron Lady'' is tough enough, but whether she is too tough. Hardly anyone, and that includes some Labour Party politicians, disputes that after five years in office Prime Minister Margaret Thatcher has replaced a sense of drift, vacillation, and expediency in British politics with resolution and purpose.
Her no-shilly-shallying approach on the Falklands crisis almost single-handedly won her a second term in office.
But while Mrs. Thatcher has few detractors when it comes to standing up to the Argentines, the Soviets, the European Community, and even to President Reagan on the Grenada invasion, there is concern that her combative style against unions, miners, and local government authorities is pushing British politics closer to confrontation and further away from its traditional course of consensus.
Even so un-British a term as ''extremist'' was on the lips of some disaffected Conservative Party voters when they left the polls May 3 in Britain's mini-elections.
The elections were not of the magnitude of a general election. They were restricted to three by-elections (special elections) for Parliament and to a host of local elections to determine the control of cities and towns in England, Scotland, and Wales. Nevertheless, the results were a scare for the ruling Conservatives.
In two of the three Conservative-held seats, the Conservative vote plummeted.
In Stafford, in the English Midlands, formerly the seat of the late and much-respected Sir Hugh Fraser, the Conservative majority was sliced from 14,277 to 3,980. The Social Democrat, who came in a strong second, was the principal gainer.
In Surrey Southwest, thought to be true-blue Tory country (affluent, with little unemployment), Conservative candidate Virginia Bottomley saw the party's majority slashed from 14,351 at the last election to 2,949 now. The Social Democratic candidate, Gavin Scott, a TV journalist, was ecstatic about his strong second-place showing, declaring that this long-impregnable Conservative bastion could be vulnerable at the next election.
Labour, in one of its traditional strongholds, comfortably regained the mining seat of Cynon Valley in Wales.
The slight increase in the percentage margin of the Labour victory in Cynon Valley reflected a fairly widespread pattern, in which the Labour Party - which was in the doldrums under Michael Foot - is making a modest recovery under the more dynamic leadership of Neil Kinnock.
These elections as a whole were the first electoral test for the new leader of the Labour Party, who is himself a Welshman.
Overall, the elections will do most to boost the morale of the resurgent alliance of the Liberal and Social Democratic parties.
When all the results were extrapolated and projected as an estimated future general election result, the Conservatives came out ahead of Labour by some 40 seats. More significantly, the Liberal-Social Democratic alliance was estimated to be capable of winning 70 seats in such a theoretical new Parliament - a delicious prospect for the alliance, since it would give it the balance of power in a hung Parliament.
Until this latest set of local elections and by-elections, the alliance had been viewed as something of a nine-day wonder.
After overtaking Labour in the polls and breathing down the Conservatives' necks in its formative stages in the early 1980s, the alliance was blown off course by the Falklands crisis and then became virtually becalmed as it struggled over the issue of its own leadership. Last week's elections suggest the alliance may once more try to assert its claim to be a major opposition force.
British politicians will undoubtedly read the results with caution. Conservatives won the last general parliamentary election with such a commanding lead that some erosion of support thereafter was considered inevitable. Midterm by-elections and local elections invariably tend to swing against the government , regardless of which party is in power. Voters also feel freer to change their voting preferences when not burdened with the responsibility of electing a whole new government in the House of Commons.
Some of the choices in these elections would have done justice to a Monty Python skit. An assortment of characters fought under such daffy political parties as ''Soon To Be Unemployed,'' ''Pro-Nuclear Holocaust,'' ''Votes For Full Hearing,'' and ''Freight Off Roads.''
Despite the ritual explaining away of these election results, the Conservatives cannot easily shrug off the setbacks since they have lost control of such important cities as Southampton, Exeter, Eastbourne, Cheltenham, Rugby, Birmingham, and Edinburgh.
Southampton was a coup for the Labour Party, because it broke the pattern of the last general election. Until this latest vote, the Labour Party had been unable to penetrate the solidly Tory south.
The loss of Birmingham, England's second largest city, was a considerable blow to the Conservatives, since its Tory-controlled council was held up as a model of local government. It had simultaneously cut local taxes and retained improved services.
The importance of local government expenditures has been underscored by Mrs. Thatcher's determination to pursue what is called ''rate capping'' here - a process whereby the central government tries to control the level of local taxes (rates) by cutting subsidies to high-spending local municipalities. The issue is rapidly building up into a major confrontation between local government authorities and the Thatcher government.
Yet neither this controversy nor the erosion of Conservative support in the cities is likely to deter Mrs. Thatcher, who appears to relish a challenge. When asked after five years in office whether she would reveal to the House of Commons her biggest mistake so far, she unhesitatingly shot back: ''There is not enough to reveal.''
Her supporters point to the rapid decline in inflation as her most significant achievement after five years in office.
Her critics charge that this has been achieved at high social cost and with record levels of unemployment. In case anyone doubts Thatcher's ability to continue the fight, she has already volunteered that she will run again in the next general election, due within five years of the last general election, which was held June 9, 1983.
Commentators seize on this as just another illustration of her determination to let everyone know that she is the boss and to eliminate any suggestion that there might be any other contenders in her party for her post.