Taking a leaf from the book of the British Tories, House Republican leaders this week will launch what they see as a 15-month election campaign against Carter administration budget policy.

Asserting that a deep tax cut is needed to curb the recession that administration and outside economists say is under way and to provide incentives for economic growth, Republicans are planning a major public relations drive to contrast what they call their "budget of hope" with a Democratic "budget of despair."

The "alternative budget" will be tested in September, when Congress adopts its second - and final - budget resolution for fiscal 1980, setting spending and revenue ceilings for the year.

At a conference of all House Republicans this week, House Minority Leader John J. Rhodes (Ariz.) is expected to make a plea for unified GOP support of the alternative budget keyed to the deep tax cut that he and other Republicans called for last week.

Rep. Guy Vander Jagt (Mich.), chairman of the Republican Congressional Campaign Committee and another architect of the new strategy, said that, whether or not Republicans succeed in changing the budget resolution in September, the debate will serve as a "dress-rehearsal" for a similar and more publicized effort in April and September of the presidential election year, when the preliminary and final budget resolutions for fiscal 1981 are up for consideration.

Party Chariman Bill Brock, who set up a meeting last week where House Republican leaders and key GOP members of the House Budget Committee agreed on the campaign, said he believes it represents a major change and advance in opposition-party strategy.

"Historically," Brock said, "any major debate in the House has broken down into its individual segments. This is an effort to talk about the total failure of the Democratic budget and our clear alternative for dealing with both inflation and recession."

The strategy is based on a study of techniques the British Conservative Party used in a lengthy expensive advertising campaign leading up to last spring's election, when Tory leader Margaret Thatcher replaced Laborite James Callaghan as prime minister.

For months, the Tories hammered the Labor tax and spending policies in parliamentary debate, and took the same economic issues to the public in simplified, dramatic billboards and advertisments.

Brock, who witnessed the windup of the British election campaign, came back convinced that the same techniques could work in the United States despite the basic differences in the two political systems.

An 80-minute film-and-narration presentation of the British Tories' campaign has been shown to GOP leaders and contributors and, last week to the House Republicans involved in the alternative budget project.

A strong independent push for the strategy has come from a grou of freshman GOP lawmakers led by Rep. Newton Gingrich (Ga.), a former history professor with an admiration for British politics.

Whether the technique can be applied here remains to be seen. Senate Republicans, led by Henry Bellmon (Okla.), ranking minority member of the Budget Committee, have taken a bipartisan approach to the congressional budget process and have not yet given their encouragement or support to the sharply partisan effort Brock and the House Republican leaders are planning.

An additional problem may be to hold key House Republicans in line behind the unified party strategy. While there is agreement in principle on the alternative budget, specific provisions will be negotiated during the August recess, after Republicans see what the Democratic majority on the House Budget Committee produces in the budget resolution markup this week.

In May, House Republicans were divided between two major alternatives to the committee's preliminary budget, and the result was that both GOP proposals failed on the floor - one by a margin of 37 votes and the other by 20.

Brock, Rhodes and Vander Jagt all said they thought there would be no such split this time.

The GOP leaders also said that pessimistic projections being offered by Democratic budget-pla;ners for next year create what Brock called "the perfect climate" for Republicans to push the budget issue to the center of the political stage.

The Carter administration's official forecast for next year projects unemployment climbing to 6.9 percent and inflation declining from the double-digit range to 8.3 percent. The Congressional Budget Office forecasts worse figures and at least nine months of overall contraction in economic activity.

Rhodes, in urging a $34 billion package of cuts in individual income taxes, faster depreciation for new investments and a postponement of scheduled Social Security tax increases, said such stimulus would boost employment and economic growth without adding to inflation or budget deficits.

That is the proposition the Republicans hope to make the centerpiece of a coordinated campaign leading up to the November 1980 congressional and presidential election. CAPTION: Picture 1, HOUSE CHIEF JOHN RHODES...will stress Republican unity; Picture 2, CHAIRMAN BILL BROCK...cites British Tories' success.