The Socialist government of Greece has submitted a landmark bill to Parliament that puts an end to a longstanding system of state control of trade union finances and reinforces the right to strike.

The bill, presented by Labor Minister Apostolos Kaklamanis two weeks ago, represents the first step in government plans to "democratize" the Greek trade union movement. The bill would abolish a central, state-controlled labor fund, financed through mandatory contributions, that dates back to 1938 and that has provoked repeated international protests.

The new legislation also abolishes the controversial Labor Law 330, passed by the rightist New Democracy government in 1976, which permitted lockouts, imposed restrictions on strikes and offered little protection to workers against dismissals for union activity.

The bill's submission is in part an effort to heal the rift that has developed between the new Socialist government and Greek trade unions. It follows months of controversy over court-enforced changes in the labor movement leadership that have brought the government into confrontation not only with international labor groups but also with the pro-Moscow Greek Communist Party (KKE).

The KKE is the third most powerful party in Parliament and its power is based in the labor force, on whose good will the Socialist government depends in its effort to revive the ailing Greek economy.

The leadership changes occurred just three weeks after the October national elections that brought the Socialists to power. An Athens court, in response to a complaint by five leftist trade union organizations, issued an order deposing the standing leadership of the Greek General Confederation of Labor. The ousted 45-member body, dominated by forces allied to the defeated New Democracy rightists, was replaced by a court-appointed leadership in which pro-government elements held the majority of seats.

The court move was denounced by labor organizations such as the European Federation of Democratic Unions, which said it would not recognize the new leadership.

It also alienated a group representing Communist-allied trade unions. The unions complained that the four seats they were granted under the court-ordered reorganization do not accurately reflect their influence in the labor movement--a view shared by independent observers.

The Communist trade unions, in line with the KKE, also have adopted a much more militant stand on the government's economic policies, criticizing budget increases as indirect taxation and accusing the government of timidity in not challenging big economic monopolies.

The Communist union leaders disagree with the new Socialist head of the labor confederation, George Raftopoulos, who says the unions will give the government a grace period through the difficult transition year of 1982 before stepping up their demands.