FRANKFURT, West Germany (AP) _ English soccer fans have begun their ''Invasion of Germany 1988,'' leaving a trail of brawls, arrests and broken beer bottles from Stuttgart to the Ruhr.

Infuriated by their national team's defeat Sunday by Ireland in the opening round of the European Soccer Championships, the English rowdies are preparing for a possible major clash with Dutch fans Wednesday night in Duesseldorf.

After the battles in Stuttgart, Prime Minister Margaret Thatcher of Britain issued a stern warning to the traveling troublemakers.

''The English Fans are Making Maggie Thatcher Angry,'' the Stuttgarter Zeitung declared Tuesday after English fans started their trek northward to Duesseldorf for the game between the England and Netherlands national teams.

It gave prominence to Mrs. Thatcher's concern that the rowdy behavior could damage Britain's business interests in Europe.

Mrs. Thatcher demanded an urgent report on the weekend violence, which resulted in 107 arrests. Most of those arrested were English.

A Stuttgart police official, speaking on condition of anonymity, told The Associated Press on Tuesday: ''Fortunately, Stuttgart is no longer the hub of the English soccer world.''

This year's soccer championships come a little more than three years after English fans attacked supporters of Juventus of Turin at Heysel stadium in Brussels. Thirty-nine people, most of them Italians, were killed in the ensuing riot.

English soccer clubs have been barred from European competition since the tragedy in May 1985, except for the national team.

West Germany's huge police operation for the two-week championship series also has focused on the Italians.

A special force of about 1,200 officers, plus helicopters, patrolled Frankfurt for Tuesday night's game between Italy and Spain.

Since European Championship play began Friday, most official attention has been devoted to the English fans, who for months have sported T-shirts emblazoned with ''Invasion of Germany 1988.''

Others drape themselves in the Union Jack, and some paint the national banner or soccer balls on their faces. Many drink throughout the day, tossing bottles on the streets.

Bobby Robson, manager of the England team, appealed to its fans Tuesday: ''Behave yourselves. Be a credit to your country and to your football team. If you don't, you are doing us no good at all.''

Mounted riot police backed by officers with dogs broke up the brawls in Stuttgart that accompanied England's 1-0 loss to Ireland.

British newspapers carried long accounts of the violence under such headlines as ''England Fans in Riot Shame,'' ''Battle in Stuttgart'' and ''Drunken Fans Give Nazi Salute.''

Police in Mannheim said one drunken English fan fell onto railroad tracks and was dragged along by an oncoming engine, suffering critical injuries.

Eight English fans were arrested Tuesday after brawling in the center of Franfkurt.

Farther north on the route to Duesseldorf, police in Cologne arrested 22 English and Irish fans who were smashing windows.

Authorities at Duesseldorf, in the Ruhr Valley industrial area, said 2,300 police officers were either on patrol or on alert. Nearly two dozen English fans were seen roaming the city late Monday, tossing empty beer bottles at stores and passers-by.

About 10,000 English and 22,000 Dutch fans will crowd into Rhine Stadium on Wednesday. Fans without tickets could increase the number of troublemakers. Dutch fans also are angry because their team lost a game 1-0 Sunday to the Soviet Union.

Police will mass in the streets when the fans head for bars before and after the game.

''The police operation prepared since February is the most important in the history of Duesseldorf,'' said Ulrich Koch, a police official and member of the special security team.