Democrat Lt. Gov. Charles S. Robb has a substantial 11-point lead over Republican Attorney General J. Marshall Coleman in their race for governor of Virginia, according to the findings of a new Washington Post poll.

Robb's showing is strongest in Northern Virginia and Tidewater, while Coleman does best in the Richmond area and in his native Western Virginia.

Nearly all of Robb's lead results from his overwhelming support among blacks. Among white voters, support is evenly divided, with Robb holding a very slight edge. But among blacks, Robb leads by more than 10 to 1.

Overall, Robb leads Coleman by 51 to 40, with 9 percent undecided. Preferences follow party lines, with Democrats strongly for Robb and Republicans strongly for Coleman. But the 40 percent of those who call themselves independents are going for Robb at this point by a 50-38 ratio. Robb also is a big favorite with women, leading Coleman by 18 percent, as compared with 5 percent with men.

At the same time, support for both candidates is soft. Among those who now favor Robb, almost half say they are not strong supporters, and fully half of those who choose Coleman say they do not support him strongly.

Many Virginians, as well as outsiders, are looking at this election as a referendum on the Reagan administration, and Coleman has linked his campaign to what he perceives as the overwhelming popularity of the president in the state.

The poll shows that 70 percent of the probable electorate approve of Reagan's performance in office. But the Reagan factor is complicated. Those who say they approve of Reagan strongly -- 45 percent of the total -- overwhelmingly support Coleman over Robb, by 64 to 27 percent.

Voters who approve of Reagan only somewhat, or who disapprove of him, overwhelmingly favor Robb. For example, 25 percent say they approve Reagan's handling of the presidency somewhat. They support Robb by 2 to 1. And the 30 percent who disapprove of Reagan's performance support Robb 8 to 1.

Cognizant of Reagan's popularity, Robb has emphasized his own conservative views and support of the president. The poll shows that voters are as likely to see both candidates as supporters of Reagan as they are to believe that only Coleman supports him. Coleman, in other words, has failed to convince many voters that if they like Reagan, they should support his candidacy.

While voters perceive Coleman as the more conservative of the two, they also see him as more conservative than they see themselves.

The poll, in which 1,633 people were interviewed, was conducted by telephone from Sept. 15 to 20. In all, 1,180 of those interviewed indicated they would vote in the Nov. 3 election, and the figures in this article are based on a "probable electorate" drawn from that group. Included as Robb supporters are 3 percent who said they are leaning to Robb; included as Coleman supporters are 2 percent who said they are leaning to Coleman.

In the lieutenant governor race, the poll shows Democrat Richard Davis with a narrow 37 to 33 percent lead over Republican State Sen. Nathan Miller, but nearly a third of those interviewed said they had not made up their minds about that contest.

In the race for attorney general, about half of those polled were undecided, with Republican Wyatt Durrette favored by 27 percent and Democrat Gerald Baliles picked by 26 percent.

Even in the race for governor, only half of those interviewed said there were importance differences between the candidates. And almost four in 10 think that both men have been changing their stands just to get elected.

A 32-year-old Richmond suburbanite says she will vote for Robb "because Coleman flips on the issues. He doesn't believe what he says, he says it only to get elected."

One issue that does seem to be making a difference is a Coleman pledge to hold the line on taxes, even if it means vetoing any tax increase that may be approved by the legislature. Robb opposes a tax increase, too, but says Coleman's position is irresponsible. Those interviewed said they agreed more with Robb on that by 3 to 1.

But if the election were held today, it would be the size of the black turnout that would be the key to Robb's margin, according to the poll. Blacks comprise 16 percent of Virginia's population, but historically they make up only 12 percent or so of the voters. If they were to vote in equal proportion to whites, Robb's margin would grow to 15 points, the poll shows. The 11-point lead is based on a probable electorate that is 12 percent black.

Although Robb has done little to woo black voters, he appears to be benefiting from the long tradition of blacks voting for Democrats.

"I've always voted Democrat," said a 49-year-old black woman from Alexandria. A 38-year-old black woman from Richmond says "the Democrats are more compassionate to the masses, and I feel Robb would be that way."

Other blacks oppose Coleman because of his close connection with Reagan. "He Coleman has a lot of Reagan's ideas," said a 32-year-old black woman from Portsmouth. "He wants to cut a lot of program, cutting a lot of money."

Coleman's hard line on crime is seen by a 24-year-old Richmond black man as "going for votes only, especially about putting so many people in jail."

While Republicans usually lead among suburbanites and high-income families, that is not the case in this election. Robb appears to be doing almost as well among suburbanites as among city dwellers, who traditionally support Democrats. And Robb leads among all income groups except for the 7 percent with incomes higher than $50,000 a year.

A 38-year-old Fairfax man with a postgraduate degree and high income finds Robb "politically aware." He says he "gets the impression that the Moral Majority is backing Coleman. And he's swinging too much on Reagan's coattails. I don't trust him."

If Coleman is having difficulty transferring Reagan's popularity to his campaign, Robb has a mixed blessing in being the son-in-law of former president Lyndon B. Johnson.

An Arlington man, 43, finds Robb "too liberal" and fears that if he is elected "the Great Society would come up indirectly" in his administration. Another Arlington man, 24, favors Coleman "for no particular reason" other than that he dislikes Robb, because "I think his whole life is structured around gaining political power."

Campaign appearances by Robb's mother-in-law didn't impress a 56-year-old Petersburg woman, who said "Lady Bird should let him run his own business. Coleman doesn't have the money backing him, so he's working harder."

But the Johnson connection appears to be helping Robb among blacks. A Richmond man, 38, finds Robb "has the style of LBJ," while an Alexandria man, 35, will vote for Robb because of "his family background with the Johnsons. He has been closer to politics in his family than Coleman."

Typical of the soft support voiced by many respondents were two women who agree the choice this year is not a happy one, but disagree on which way to vote. A 60-year-old Williamsburg resident picks Coleman "as the best of two evils," while a 68-year-old Richmond voter goes for Robb as "the lesser of two evils."