FOR many decades Britain's cartoonists have depicted the country's trade union movement as a resolute old cart horse. But Tony Blair, leader of the Labour Party, must be tempted to see it as a cantankerous mule.
Youthful and telegenic, Mr. Blair already has been strategizing for some months to end a decade and a half of Conservative rule in the next general elections.
But Britain's big unions are blocking his victory. To win broad middle-class support, Blair has repeatedly tried against their will to ditch Labour's Marxist roots -- and specifically to abolish the party's commitment to the state ownership of industry. A special party conference on April 29 may be the final showdown between him and unions, which provide the bulk of Labour's income and its organizational base.
Clause 4 of Labour's constitution, which dates from 1918 and is printed on the back of every party membership card, commits Labour to ''the common ownership of the means of production, distribution, and exchange.''
Blair has even taken a series of ''road shows'' around the country to convince the party faithful that getting rid of Clause 4 in its present form will make his party ''fit for government in the 21st century.''
He and other party modernizers compare Labour with Germany's Social Democrats, who abandoned Marxism in the 1950s and began winning over voters who balked at hard-line socialism.
But powerful union leaders have other ideas, keeping their grip on political power even though union membership fell by about a third during the Thatcher years of the 1980s, to about 8 million today.
On April 13 delegates of Unison, Britain's largest trade union with 1.3 million members in health services and local government, voted 55 to 47 to keep the clause as it stands.
Earlier, Bill Morris, leader of the Transport and General Workers' Union (TGWU) -- the second largest of organized labor's ''big battalions'' -- urged his followers to reject a heavily redrafted version of the clause in mid-March, which makes no mention of nationalization.
If the two unions hold to their present course, they will command 25 percent of the vote at the April 29 meeting. Geoff Martin, a Unison delegate and a member of a Defend Clause 4 Campaign said: ''The [Unison] vote proves that Tony Blair cannot ride roughshod over the trade union movement.''
TGWU leader Morris has said he might back the new Clause 4 in return for a Labour promise to endorse a minimum wage of 4 ($6.40) an hour. Rodney Bickerstaffe, leader of Unison, reportedly backs Morris's demand. Other union leaders say they might be prepared to support Blair if he rewrote the clause to include a commitment to full employment.
But a Blair strategist said the Labour leader was unwilling to engage in ''horse-trading,'' since that would ''persuade many voters that the party under his leadership is mired in its old policies.''
Labour hopes to win over many Conservative voters by making it plain it thinks nationalization is in the past. Blair's advisers say he is convinced that if he gives in to the unions over Clause 4, Labour's chances of winning office two years from now will be seriously jeopardized.
''Even if we won after giving ground to the unions,'' a Labour official said, ''he would have signaled to them that they can still command our policies.''
For now, Blair is promising ''fairness but no favors'' to unions. But he is having to contend with pent-up frustration among union leaders, who have waited through 15 long years of Conservative rule, when they have been unable to influence government but could hope that, under Labour, life would be different.