The anchor man of BBC radio's Today program, which wakes up the British establishment with the news each weekday, pushed back from his microphone after a long morning's coverage of the attempted assassination of President Reagan, which occurred the night before on London time.

"Is everybody over there crazy?" he asked a visiting American. Forming his fingers into pistols, like a small child playing cowboys and Indians, he waved them about menacingly saying, "Pow, pow!"

Prime Minister Margaret Thatcher's press secretary anxiously studied the latest news service report on the condition of the president's press secretary, James Brady. He shook his head. How could the affable man he had met just a few weeks earlier on Thatcher's trip to Washington be fighting for his life with a bullet in his brain, he wondered.

Another Thatcher aide was visibly angry. He demanded to know why the world's leading democracy, its allies' protector and indispensable economic partner could repeatedly allow its leaders and its government to be endangered this way. It will happen again and again, he lectured, until Americans do something about guns.

Leaving aside the shrillest, crudest editorials, cartoons and innuendos in the tabloid press here depicting the United States as overwhelmed with guns and violence, disturbing images dominated the most evenhanded British media reports from Washington this week: long lists of American public figures killed, wounded and threatened by assassins since the 1960s; the ease with which still another mentally disturbed young man could repeatedly arm himself and allegedly stalk a public figure; the obvious failings of the FBI and the Secret Service following his first arrest and allowing him so close to the president; and apparent sickness in a society that make relevant and believable the exploitative tawdrines of a film such as "Taxi Driver."

The amazing thing, the Washington correspondent for The Times of London told readers here, is how Washington seems to make it all in stride. It has become so familiar: the endlessly repeated replaying of the shooting on television, the gunman's wild fantasies made real, the fruitless arguments about gun control.

"The country will be back to normal quickly enough," he concluded with knowing British smugness.

The fact is Britain has little to be smug about these days. It, too, seems unable to come to grips effectively with increasingly disruptive soceital problems, not the least of which has been an alarming increase in violence: Businessmen robbed at gunpoint on busy London streets. The Yorkshire Ripper's multilation murders of 13 young women in industrial cities in northern England. Neo-Nazi white gangs attacking Asian immigrants in London's East End. Blacks clashing with police in rioting last year in Bristol. Attendence at soccer games plummeting because of masses of drunken hooligans brawling in the stands.

The unceasing sectarian violence in Northern Ireland also has spilled over into the rest of Britain and Ireland with bombings and assassinations. Lord Mountbatten, a celebrated military hero and cousin of the queen, and Airey Neave, a senior politician and confidant of Thatcher, have been among the victims.

Yet the vast majority of Britons still feel safe on their streets. London, with a population of 7 million, had 179 homicides last year, compared to 1,557 in Los Angeles and 1,733 in New York. Guns were used in only 750 robberies in London last year. Most police officers still do not carry guns, and London police officers specially authorized to use them in certain circumstances fired shots on only eight occasions last year. Permission is seldom granted for private ownership of a handgun by anyone, and possession of a rifle or shotgun requires a license granted only after review and approval by local authorities. r

Despite disturbing signs of growing alienation in the current generation of young Britions facing the worst employment prospects since World War II, general attitudes here toward violence and guns remains noticeably different than in the United States.Although there is an undeniable tendency in this declining nation to jump on every sign that its rich cousin may have worse problems, exasperation and bewilderment here about this latest assassination attempt are genuine and run deep.

"American citizens, crying, 'Oh no, not again,' at news of this latest near-fatal shot, must be made to realize that restrictions on the ownership of handguns can have more real impact on this problem than all the cumulative shame about the rise of violent crime in the U.S.," concluded the Financial Times, perhaps Britain's most respected and thoughtfully conservative newspaper. "Nor would it be an unwarranted intrusion of America's allies to say as much. The safety of the American leadership, and of the U.S. president in particular, is of much more than national importance."