London — Spectacularly and insistently, unsolved problems are hammering at Britain's door, demanding solution.
An ancient society is once again confronted abruptly with the modern world of violence, and weaknesses and historic divisions are spotlighted - all the more dramatically now in the wake of victory in the Falklands and the calling off of two recent train strikes.
Even as a number of trade unions show signs of adjusting to the new world, pessimists here say other British institutions and upper-class establishment attitudes have been found wanting, and remain out of touch with the needs of today.
Optimists, including Prime Minister Margaret Thatcher, reply that weaknesses can be tackled with success if Britain pulls together with a ''Falklands spirit'' in the face of new challenges.
Startling the nation have been:
* A reemergence here of the sectarian hatred of Northern Ireland as the Provisional wing of the illegal Irish Republican Army (IRA) took responsibility for the first of two tragic explosions in Hyde Park, central London, July 20. Another bomb went off in Regent's Park some two hours later.
Altogether, nine people were killed and almost 50 injured. Windows were blown out and thousands of people in London heard the first blast, causing immediate police fears that Britain was in for a long, hot summer of IRA violence.
* Glaring breaches in security procedures in high places continued to come to light, causing incredulity in the House of Commons and revealing the need for urgent reforms.
Upper-class disdain for ''Reagan-type security'' is now yielding to belated recognition that, sad as it may be, traditional British reliance on old school ties and gentlemanly ways will no longer do.
Security clearance procedures for senior security work has been shown to be seriously at fault in the case of Queen Elizabeth's personal bodyguard, police Commander Michael Trestrail. He has just resigned after revelations that he had been engaged in homosexual activities for the past 15 years apparently unknown to security officers.
If this was not bad enough - coming as it did after an unemployed man, Michael Fagan, easily evaded lax Buckingham Palace security July 9 and spent 10 minutes talking to the Queen in her own bedroom - yet another security lapse has been unearthed.
This involves the top-secret government communications center at Cheltenham, which eavesdrops on other countries and shares intelligence with the US. Taxi driver Geoffrey Arthur Prime has been charged with unspecified acts of espionage over the past 13 years, raising speculation that this could be the worst security leak here since the days of Burgess, Philby, and Maclean. Prime is said to speak Russian.
* And the dislocations of decades of British industrial decline and slowness to adapt to new technologies rose up anew July 20 with the announcement of the worst unemployment figures in Britain's history.
An expected but still startling jump of 76,000 school graduates unable to find work since last month pushed the total out-of-work figure to 3,190,620. A total of 304,000 young people are out of a job. While that figure is expected to fall somewhat after the summer vacations, adult unemployment is expected to go on rising for months to come, government officials concede, despite strenuous retraining schemes.
Thirty thousand jobs are being eliminated each month now and their occupants ''made redundant,'' in the British phrase. Meanwhile, vacancies are not rising noticeably. The prime minister was forced to concede to the House of Commons late July 20 that the figures were ''very disturbing.''
This is a time of strain and stress for Britain. The Falklands victory has clearly heartened Mrs. Thatcher and her Cabinet and led them to be tougher with trade unions and on holding down government spending.
Yet the nation is being tested in a number of areas and answers are urgently required.
The IRA bombing may have been in response to the conviction of IRA member Gerard Tuite recently. At this writing, no one seemed sure.
Certainly the Hyde Park bomb was designed for maximum horrific effect. Most of central London heard the tremendous blast. It rattled windows up to a mile away. Clearly aimed at the military, at royalty, and at the British establishment all at the same time, the bomb detonated in a car just as the Royal Household Cavalry, Blues and Royals Squadron, was leaving for guard duty at Buckingham Palace.
The second bomb went off beneath a bandstand in Regent's Park while the Royal Greenjackets band was playing a lunchtime concert. Eyewitnesses at both places could hardly describe the scenes of death and devastation.
The prime minister condemned the bombings in the House of Commons July 20 as ''callous and cowardly crimes'' committed by ''evil and brutal men who know nothing of democracy.'' The government would not rest, she said, until they were brought to justice.
The case of Commander Trestrail opens up a range of basic questions about the way officialdom works in this country. How, members of Parliament want to know, could a 15-year homosexual involvement have failed to come to the attention of those officers in the Home Office, the Special Police Branch, the MI5 intelligence service, and the Foreign Office, all responsible for carrying out security clearances?
The involvement, now considered a clear security risk in itself, casts doubt on the effectiveness of the security clearances given to a total of 68,000 government posts in Britain. In May, the security commission headed by Lord Diplock recommended that homosexuality itself not necessarily bar a man to high office in the civil service. But police officials still regard it as an invitation to blackmail.
As for the Cheltenham communications center, it is one of the most sensitive in the world, linked to the US, Australia, and New Zealand in sharing intelligence information.