The National Front, an openly racist organization with a growing appeal for Britain's distressed workers, today gave an ominous display of its gathering strength.

About a thousand Front members, waving Union Jacks and singing "Rule Britannia," defied a counter-rally organized by Labor and leftist forces to keep them off the street. The front men and a sprinkling of women marched three miles through North London boroughs heavily populated with West Indian and Asian immigrants.

The marchers were protected by flanking walls of police, perhaps 1500 strong, and a dozen mounted policemen. But the Front, dedicated to driving immigrants out of Britain, made its point.

The frustrated Labor-leftists hurled bricks, bottles, tin cans, eggs, flour and smoke bombs at the marchers. They cursed them as "facist scum" and "bastards." But they failed in their stated objective, to push the Front off the streets.

There were frequent scuffles as the counter-demonstrators tried to break through the police lines. The Scotland Yard men, who along with journalists were the principal victims of the missiles, were remarkably cool, however. For the most part, they kept the two antagonistic forces apart.

By nightfall, 60 persons had been arrested, five policemen had been treated for cuts, and half a dozen marchers were wearing bandages.

This drama, at sharp variance with the civility that prevails in most of Britain, cannot be dismissed as an incident of no consequence. The fact is that the Front, with its middle-class leaders and its worker rank-and-file, is now a political force to be reckoned with.

At a Birmingham by-election last month, the Front displaced the Liberals as the third party and collected 8 per cent of the vote. It might have done better except that the winning Tory stole some of the Front's thunder, ignoring the official Conservative line and coming out flatly against any further immigration.

In some recent local London election, Front candidates have polled as much as 17 per cent. There will be many more local elections all over Britain May 5, and the Front total will be closely watched. For the first time, the extremist organization is running candidates for 91 of the 92 seats in the Greater London Council. The Front is not likely to win any but could top 20 per cent in some areas.

The organization is 10 years old but has come to life only in the last three years of a worsening economy. Rising jobless queues, raging inflation and sinking living standards for workers have nourished the Front. Inevitably, some are led to believe that blacks, Asians and Jews are the source of their misery.

The Front does not have much of a program, save for hostility toward those who are "not British." Today's march ended in the jammed assembly hall of a school in Arnos Grove where speakers denounced a variety of targets.

The press was sneered at Leaders of traditional parties were called "rats" or "homosexuals." Margaret Thatcher, the Conservative leader, was described as "Edward Heath in drag." "International bankers" were hit and there were jeers or boos at references to Israel, Tel Aviv and the Jewish Board of Deputies.

But the central' target was identified by Martin Webster, the Front's 34-year-old "national activities organizer," who shouted:

"If they're black . . ."

"Send them back," the hall roared with one voice.

The Front's national chairman is an unimpressive, balding, middle-aged man, John Tyndall.

He has the knack of building his voice to a hoarse cry at each climax. He delighted an audience that thrilled to melody rather than words.

Tyndall said:

"I've watched this grat city degenerate - it's getting to look like one colossal slum - it could be a capital of Jamaica, India, Pakistan, Cyprus, Israel." (Applause and laughter.)

"There are no-go areas where law-abiding white people fear to tread. That's because the best Londoners move out and all the refuse of the world moves in." (Roaring applause.) "The answer is - send them back."

Tyndall brought the crowd to its feet with this:

"You Reds, you people of the left, you scurvy scum, you will not stop us. In the ranks of our movement marches the spirit of a great people . . . determined to march forward and take back our country."

The rallies began and most of the incidents took place in Haringey, a pleasant, tree-shaded North London borough whose Labor mayor, Vice Butler, was on hand to support the Front's foes. So were some of his Tory opposition councilmen.

But Butler was visibly upset by the bitterness and hatred generated in his backyard. From time to time, he fingered the gold mayoral chain he wore and its medal with the motto, "Progress With Humanity."