Violence by Irish Republican Army terrorists determined to drive Britain out of Northern Ireland is increasing again.

The upsurge follows a long period during which British and Ulster security forces, coordinated by Britain's tough-talking Northern Ireland secretray, Roy Mason, have been achieving some success in reducing the violence and frustrating the IRA with improved intelligence, surveillance and security techniques.

But now attacks are increasing and the IRA has vowed to attempt to disrupt the forthcoming British election campaign with more violence in the rest of Britain as well as Ulster.

Recent incidents include a bombing attack Thursday night in which 31 explosions damaged banks, shops and government offices in 17 Northern Ireland communities. A week ago, a British soldier was killed in Armagh Country near the Irish border, and shortly before that the 9-year-old daughter of an Ulster policeman was seriously wounded by a bullet apparently intended for her father and two teen-age boys were killed by a bomb.

Before the new wave of IRA violence began last November, terrorism-connected deaths had decreased two years in a row to a low of 77 in 1978. A number of terrorist murder cases were closed with convictions, putting into prison murderers including a Protestant gang that had stabbed, shot and garrotted a number of Catholics at random and, in a sentencing last week, a Catholic IRA member who alone had committed four murders.

To emphasize his frequent public assertions that "normality is gradually returning to the province," Mason reduced the number of British troops on duty in Ulster to fewer than 13,000 from a high of 21,000 in 1972, when Britain took direct control of government and security from Northern Ireland's formerly Protestant-controlled parliament.

Street patrolling has been mostly shifted from the soldiers to Ulster police officers. The huge steel security barriers around central shopping districts have been taken down in a number of cities and towns.

But the past week's violence, as an IRA spokesman declared, has contradicted Mason's "claims that we're a spent force."

The IRA appears to have access to plenty of explosives, more sophistication in handling them, ample funds from bank robberies and sufficient manpower to carry out a widespread attack like Thursday night's bombing raid.

After 10 years of IRA terror and the presence of British troops in Northern Ireland, everything is far from normal.

There are still military checkpoints on some roads and surveillance helicopters circling overhead. Everyone entering the airport, train station or central shopping district of Belfast must submit to repeated searches.

Unemployment in Ulster is double the rate for Britain as a whole. Proportionally, more than three times as many families in Ulster are poor enough to receive welfare payments than in the rest of Britain. Thousands of Bel-fast residents live in housing officially deemed unfit to occupy. At the same time, block after block of houses stand vacant and boarded up, abandoned by Catholics fleeing Protestant neighborhoods and Protestants leaving Catholic areas.

Mason, who made security and the economy his top priorities as Northern Ireland secretary, also has made some strides on the economic front. With tireless traveling to attract British and American firms to Northern Ireland, he has won commitments for plant expansions and new industries that will produce 5,400 new jobs, although it may cost British taxpayers as much as $100 million for inducements that landed the 2,000 jobs in the De Lorean sports car factory under construction outside Belfast.

But Mason's 2 1/2 years in charge of Ulster also have been marked by a lack of progress on the political front. No meaningful discussions with Catholic and Protestant leaders on even a short-term alternative to "emergency" direct rule by Britain have taken place for many months.

Until the recent violence and controversies over the treatment of IRA terrorists in police interrogation centers and Ulster prisons, Northern Ireland had been a forgotten issue in British politics and media.

Referring recently to this long silence despite the bombings, continuing presence of British troops on Ulster streets, and a five-year-old "emergency" suspension of some civil liberties for terrorist suspects caught anywhere in Britain, John Hume, deputy leader of the Catholic Social Democratic and Labor Party in Northern Ireland, said. "If all this was happening in any other part of the United Kingdom, it would be a burning issue, and a daily one until it was resolved."

The party, considered a crucial vehicle for moderate Catholic leadership in Northern Ireland, has become increasingly frustrated by a lack of movement toward increased representation of Ulster's Catholic minority in the British Parliament and any future government in Northern Ireland. Its leaders are particularly unhappy that the Protestant Ulster Unionists, who hold 10 of the 12 Northern Ireland seats in Parliament, have won approval for five new Ulster seats with the expectation that most or all will be filled by Protestants.

Ulster's Catholic leaders strongly believe that neither the ruling Labor Party nor the opposition Conservative Party is eager to press for a political solution in which the Protestant majority would have to share power proportionately with Catholics, because both parties seek the support of Ulster's Protestant unionists.

This also is the belief of political leaders in Ireland, who have been cooperating with the British in the battle against the IRA and have tried to appear patient in their desire to see Ireland eventually unified.

Irish Prime Minister Jack Lynch has renewed his call for "political direction from the British government" to search for an Ulster solution. And the leader of the Irish opposition, Garret Fitzgerald, has suggested an interim confederation of Ireland and Ulster for security, economic development and international relations, with home rule maintained in Ireland and Northern Ireland for most other functions.

In an argument that Lynch later supported, Fitzgerald pointed out that recent rapid growth in Ireland has made it a more attractive economic partner for Ulster, and that in their relationship with the European Economic Community, each has more in common with the other than with Britain.

The British government has responded to this suggestion with silence.

It is clear to leaders in Britain, Ireland and Ulster that little can be done on the Northern Ireland political question until after a new British government is elected this year, with what Irish and Ulster Catholic leaders hope is a big enough parliamentary majority to be free of dependence on the Ulster unionists.