The moaning and groaning started while I was still on the North American side of the Atlantic. "So you're going to London," said a recent visitor. "Well, don't take clothes, take money."

"If I sell my mother-in-law's pearls, I think we can all go out to dinner," wrote a friendly native.

"I can't get over how cheap things are here!" raved a touring Briton eyeing $3.50-a-pound sirloin at my supermarket.

With smoke signals like these, you have to be pretty thick not to get the message. But this winter's cut-rate standby fares beckoned and I reckoned: Surely a country that once landed men on the moon can still send tourists to Piccadilly.

It can. It's just that when middle-income Londoners define a "bargain" as a restaurant where you can eat for only $20 a head and call hotel doubles for $75 a night "a real steal," the traveler tied to a shorter shoestring should understand that comfort isn't going to come without a struggle.

The news is that a lot of Londoners suddenly want to help. The city's reputation as only fit for oil sheiks has begun to hurt. Tourism this past summer was termed "disappointing." The middle-spenders were missing -- and much missed. The result is a plot to encourage them to come back and try again.

I got a strong whiff of what was in store when I dialed British Airways about a ticket. Instead of listening to music while I waited to be connected with a resevation clerk, I got a recording alerting me to special new bargain hotel rates available at the last minute to standby -- and other passengers. I already knew about similar offers from other airlines.

There was some kind of foul-up, however, and although the airport clerk cherrily confided that "this hotel thing is a really good deal," he couldn't find any list of availabilities. I had to do without.

It was an easy flight, though, and I had the strength to call a half-dozen small, Brand-X hotels to see if any of them truly loved me. Four instantly assured me that, yes, they probably could make reduction in price for a stay of a week or more. Nonetheless, the more I thought about it, the more I inclined toward taking a "service flat."

Service flat is British for a short-term, furnished apartment with regular (often daily) maid service. They come in all sizes and shapes, not to mention prices, and some are listed in the booklet "London Hotels and Restaurants, Including Budget Accommodations," available by mail for $2.50 from the British Book Shop, 680 Fifth Ave., New York, N.Y. 10019. You can also direct specific questions to the British Tourist Authority at the same address. The trouble is that you can't get much in the way of critical appraisal, so regardless of how large they write words like "luxury" and "deluxe," you haven't a clue about what you'll get until you see it.

After inspecting one ugly little "luxury" number whose only justification for a claim of class was its address, I fell back on two spots I already knew, Nell Gwynn House and Chelsea Cloisters, both on Sloane Avenue, close by Upstairs, Downstairs land, the golden ghettoes of Knightsbridge and Belgravia.

Nell Gwynn is easily the more attractive of these two large, modern, multi-unit buildings, but one month was their minimum rental period, and 100 pounds (about $245) a week was their minimum price. Chelse Cloisters was 65 pounds a week (about $160) and agreeable to a 22-day stay.

The last time I'd tried Chelsea Cloisters, it looked in urgent need of an exterminator and considerable soap and water. Fortunately, it appears to have got both, and even if it's still not ready for all-out cleanliness freaks, I am nothing if not flexible when a place provides reliable heat, color TV, unlimited hot water, a private bath and a convenient location -- all at a price I'm prepared to pay.

Of course, it also had one other big item. There was a kitchenette with a hot plate, dishes and a tiny refrigerator. With after-dinner coffee going for roughly 75 cents to $2 a cup in restaurants above the cafe level, a snack shop to call your own has clear-cut economic advantages.

What to do to make London affordable if you don't want a flat and don't sign up for a discount hotel deal before arriving? Well, you could do a lot worse than to go immediately to any London or British government tourist office to see a copy of "Let's Go," a catalog of reduced-rate "winter break" midweek and weekend hotel offers. You would then discover that middle-spenders who like their comforts can again get a pretty fair shake for at least two nights and, the way occupancy rates have been going down, possibly longer.

Samples: on a two-night plan, a double room with private bath, continental breakfast, service and taxes is 16.75 pounds (about $40), at the Cranley Gardens, 8 Cranley Gardens, SW7; the Hyde Park Towers Hotel, Inverness Terrace, W2; and the Viceroy Hotel, Lancaster Gate, W2. For 13 pounds (about $31), there's the Stuart Hotel, 110 Cromwell Rd., SW7. For 20 pounds (about $48) per night on weekends, you can stay at the Vanderbilt Hotel, 76 Cromwell Road, SW7.

Newsworthy note: In many instances, the single room rate is exactly half.

If you're willing to forgo all frills, the London Tourist Board says its Victoria Station hotel reservations office has beds as low as 4.50 pounds a night (about $11) and the average price paid by visitors who used the service last summer was six pounds (about $15).

I didn't want to give up anything I wasn't forced to, though, including eating in "serious" restaurants and seeing the sights that are far from free -- for instance, "Evita" and the other hot tickets on the London show circuit. I did stick to only one restaurant meal a day and sacrificed taxis (even the radio-called minis rarely cost less than $3 a trip).