Problems assail Britain's 'Iron Lady' as Tory party convenes

Suddenly, the ''Iron Lady'' and her government look vulnerable. When Margaret Thatcher swept to a massive general election victory four months ago, that thought was unthinkable.

But as the Conservative

Party gathered at Blackpool for an annual conference planned as a celebration of success, the prime minister was under pressure from several sides.

Most immediate of the problems assailing her was the revelation that Cecil Parkinson, one of her closest ministerial colleagues, had had an affair with his secretary, who was expecting his child.

Mr. Parkinson, Tory party chairman until a month ago, is battling for his political life. Mrs. Thatcher appeared to have no option but to support him in his wish not to resign because of the scandal.

While Tories in the shires were pressing for Parkinson's removal, an ideological bombshell landed. The youth wing of the Tory Party, press leaks indicated, had compiled a report alleging infiltration of Conservative ranks by extreme right-wing groups bent on gaining influence over party policy.

The report was so detailed, mentioning more than 100 instances of ''fascist entryism,'' that the new party chairman announced strict new rules for the selection of Tory parliamentary candidates.

And leading figures in the party openly challenged the economic and social philosophy of Mrs. Thatcher's government.

Francis Pym, sacked as foreign secretary after the June election, criticized cuts in public spending and worried aloud about a weakening of traditional Tory commitments to compassionate politics. John Biffen, leader of the House of Commons, joined those saying Mrs. Thatcher's policy of slashing health and social services has gone far enough.

Conservative Party conferences are well-managed occasions, and attempts were under way in Blackpool to minimize the damage to Mrs. Thatcher and her reputation for resolution and sound judgment. Parkinson appeared on television, insisted that he would continue in office, and claimed that he had widespread support for doing so.

Mrs. Thatcher's critics in the Tory Party had been silenced by the scale of her June victory. Now they are questioning her judgment in placing such trust in Parkinson for so long.

Ironically, Mrs. Thatcher has depicted the Conservative Party as a party of rectitude and deep commitment to the family. In this context Parkinson's conduct may have done considerable damage to Tory support in the countryside.

It is widely considered that Parkinson's political career will start to decline, even if he manages to weather the present storm.

Developments within the opposition parties made the prime minister's position appear even more exposed. The Labour Party, under its new leader, Neil Kinnock, put on a display of apparent unity at its party conference in Brighton. The Liberal Party under David Steel and the Social Democrats led by David Owen have cemented their political alliance.

None of this means the Tories are on the verge of collapse. But the indications are that Mrs. Thatcher will have to battle to restore the credibility of her leadership and judgment. For the first time since the Falklands war, the ''Iron Lady'' is on the defensive.