Britain's first rule of canvassing. 'Shut the garden gate ...'

It is the homely touches that are so appealing as the June 9 election approaches here: The Labour candidate, apologizing for having no milk for our late-afternoon tea, who nipped around the corner from his committee headquarters to buy both of us half a pint in a cardboard carton. . . .

The battered card tables with holes in the top that held campaign literature in a run-down, seen-better-days committee headquarters for a Conservative member of Parliament in a north London seat. . . .

The Social Democrat who took me to his own swing constituency in Birmingham on the top deck of a bus. His car had broken down and he had no other way to get there. . . .

British grass-roots campaigns are run differently from their counterparts in the United States. Spending is strictly limited by a law which confines candidates to raising about (STR)4,200 ($6,720) for the average candidate. So in Britain's newly redrawn 650 constituencies, campaigns for the nation's 42.7 million voters are run on shoestrings.

There is one big loophole: Party headquarters in London can send in big-name speakers and put up posters outside the local cash limit. This helps the wealthy Tories and works against the poorer Labour Party and the alliance of the Liberals and Social Democratic Party (SDP).

Meanwhile, in this small set of islands, where many voters do not own a telephone, the backbone of the campaign remains the methodical canvassing of individual houses and flats (apartments) in search of the ''doorstep vote.''

Tory candidates say this doorstep vote mirrors the national polls, which show Prime Minister Margaret Thatcher well in the lead. Labour contenders say it shoots holes in the national polls by revealing large numbers of undecided voters who will eventually return to the Labour fold. SDP-Liberal alliance campaigners insist floating Labour voters will turn to the alliance.

Whatever way they are interpreted, doorstep campaigns do show volunteer democracy in action. Candidates are helped by party faithfuls, who take time from their jobs (in the north some are unemployed) who prepare lists of names and addresses for every street, and who sometimes canvass in advance as well.

In the last three days I have ''doorstepped'' with three candidates in two big cities. We talked with 60 to 70 householders - young, old, black, white, wealthy, poor. Overall impressions include:

* The growing impact of television, which highlights national party leaders and issues but gives short shrift to local issues and local candidates.

''Much depends on how voters in our area react to national leaders as they appear on television,'' admits Labour Party worker Chris Kirk in Birmingham. This helps Mrs. Thatcher and young, articulate Liberal leader David Steel, but hurts the older, less telegenic Labour leader Michael Foot.

* Campaigns are becoming more presidential in the US style. National leaders bask in TV and press attention. Personality and charisma count for more and more. At the grass roots, workers fear that solid issues are counting for less, swamped by the way issues are made to appear in the hands of national leaders on the ''telly.''

* Thirty percent of those interviewed said they were still undecided. A large percentage were worried about local issues: insurance claims, street lighting, low pensions. In Birmingham, former Labour voters said again and again they were upset by the party's infighting, by its defense policies of giving up nuclear weapons, and by leader Michael Foot's ineffective TV image. Several men and women came to their doors to express a fear of communism. No one talked about taxes or ecology or a host of other issues.

* The three-week campaign is so short, and the political system here so adversarial, that many people are confused by the ceaseless barrage of charge and countercharge, attack and counterattack, pouring out every hour.

* Public opinion polls are setting the pace. ''People like to vote for a winner,'' says Labour candidate Jack Turner in Selly Oak, Birmingham. ''This is helping the Tories.''

''What you hear time and time again,'' says SDP candidate Chris Barber in Birmingham's ''marginal'' (narrow majority) Erdington seat, ''is people echoing the polls. People tell me they'd vote for me . . . if they thought I could win.''

The result: Barber's chances largely depend, not on his own reputation as a veteran local politician, but on the success of alliance leaders in London convincing the news media that they have a real chance of gaining at least a share of power in a ''hung'' House of Commons. He could be beaten by a new generation of politician, a 27-year-old Oxford graduate standing for the Tories, if Mrs. Thatcher's national swing is great enough.

Meanwhile, going door to door has a mood all its own.

''The first rule of canvassing,'' said Conservative MP Hugh Dykes briskly as we half-walked, half-sprinted down an endless road in Harrow East near London, where he holds a seat, ''is, shut the gate behind you. People don't like it left open. . . .''

''That's right, but you mustn't walk across front lawns either,'' said Jack Turner, a former bricklayer and furnace designer, as we slogged through the late afternoon in a public-housing estate in Selly Oak.

As Turner pushed open a porch door in Flax Gardens, a small irate dog flew out, followed by an only slightly less irate elderly woman. He calmed her down, listened sympathetically while she told how she had to live on a widow's pension of (STR)33, 75 pence ($54) a week, then turned to me and grinned. ''Don't let dogs out, either,'' he said.

''And you can forget about holding public meetings,'' added Social Democrat Chris Barber. ''People just don't come. They say they are busy, or they want to watch TV, or go to the pub. . . .''

The tall and clipped Mr. Dykes, his blue blazer resplendent with campaign stickers, says he has given up public meetings altogether. The Tory central party office thinks he will win the Harrow East seat, so it would send him only junior ministers as speakers.

Jack Turner's seat in Selly Oak, however, is regarded as so crucial by the Labour Party that it has been visited by Michael Foot (who drew what party men say were 700 people), deputy leader Denis Healey (600), and leadership hopeful Neil Kinnock (400).

In Harrow East, the largest constituency in London with 80,539 electors, Conservative Mr. Dykes runs a well-oiled campaign from a blue loudspeaker van donated by a supporter and driven by a volunteer aide.

In Selly Oak, bearded Labour candidate Jack Turner drives a battered Ford sedan to local working-class streets and then goes door to door on foot.

In Erdington, Social Democrat Chris Barber suffers from a lack of skilled canvassers to pave his way. The SDP only came into existence after the 1979 elections. His headquarters are in a jeweler's shop, rented for the campaign.

Only 66 of the former 635 constituencies remain intact after a thorough redrawing of electoral boundaries. The changes reflect the drift of people away from the urban areas (down 16 seats) to the shire (rural) counties (up 23). This is good news for the Tories, whose net gain should be 21 seats, and bad for the Labour Party.

To win the election, Labour must gain at least 66 new seats - a swing from Tory to Labour of 5.5 percent of all votes. No party since 1945 has achieved such a swing. The Tories regained office in 1979 on a swing of 5.2 percent.