THE hunt is on among Britain's ruling Conservatives for ways to make their party attractive to women. Success or failure may help decide the next general election.Prime Minister John Major has, in polls, scored well among women. But the Conservative Party as a whole is perceived as less attractive than the Labour opposition on issues affecting women. With their eyes on July 1992 as the latest possible general election date, strategists at Conservative Central Office say they are concerned by research showing younger women may need much persuading not to vote for the opposition Labour Party. Strategists have advised Chris Patten, the Conservative Party chairman, to move quickly to combat Labour's determined bid in the last two years to portray itself as the party defending women's rights and extending women's role in politics. "So far Labour has been twice as active and twice as successful in choosing women parliamentary candidates," a Conservative Party official said. "It is also pushing women into senior positions in the shadow cabinet. We have to begin matching that." Mr. Patten is pressing Mr. Major to appoint a woman to a job in his own Cabinet. The prime minister's decision not to name a woman to a top post when he assumed office in December was criticized by party officials who had hoped to be able to point to a more enlightened approach. Margaret Thatcher, in nearly 12 years as prime minister, never appointed a woman to her Cabinet. Jack Cunningham, Labour's election campaign coordinator, says Major's failure to choose a female Cabinet member "underlines the government's continuing lack of understanding of women's needs." Mr. Cunningham said Labour has selected 140 women candidates for the 640 seats to be contested at the general election. Conservative Central Office confirmed Monday that the government party would probably field just over 60 women. "We have committed ourselves to increasing the number of women in the Labour Party national executive, and there are four women in Neil Kinnock's shadow cabinet," Cunningham said. A Labour Party official says the party hopes "to achieve a 40 percent threshold for women in most key areas of party activity." A resolution to that effect will be voted on at the Labour Party's annual conference in October, the official said. Major enjoys one advantage over Neil Kinnock, the Labour leader: He is personally popular with women voters, whereas Mr. Kinnock is significantly more popular with men than women. But in areas such as foreign affairs and the British economy, Major still enjoys a comfortable edge over Kinnock, says Robert Worcester, head of the MORI polling organization. So far Major has taken two steps to correct the perception his party has been slow to appoint women to top posts or listen to what women want. Last month he asked Sarah Hogg, head of his policy unit at 10 Downing Street, to review Conservative policy towards the family. Mrs. Hogg is the first woman to direct the policy unit. Angela Rumbold, a junior minister at the Home Office, has been asked to travel around Britain and obtain women's views on what the government should be doing to meet their needs. Some Conservative insiders say the most persuasive thing the prime minister could do, given the few months until the general election, would be to appoint at least one woman to the Cabinet. There have been press reports that Major may decide to promote a woman to his Cabinet in the fall. Major and Patten are said to be worried by a new MORI survey suggesting that younger women tend to prefer Labour policies. MORI found that twice as many women as men aged 18-to-24 years say they will vote Labour. Research shows that nine out of 10 single parents are women, and that most are impressed by Labour promises to raise child benefits and give children of working mothers guaranteed places in nursery school. The Conservative Party has tended to be identified with curbing state spending on social security services, including child care.