It's the kind of thing world travelers like to boast about, and the couple from New Jersey was no exception. Gleefully they told of shaving roughly $50 apiece from the lowest air fare offered them to Copenhagen. They did it by using the London Connection.

By "London Connection" they meant that when they couldn't find a charter from the United States nor meet the several-months-ahead purchase requirements attached to the cheapest fare offered by the scheduled airlines, they did what lots of dedicated American cost-cutters are doing. They grabbed one of the new bargain fares to Britain and then bought another cut-price excursion from London to Copenhagen.

Unfortunately, such stories don't always have happy endings. In addition to the pitfalls outlined in last Sunday's article, there's the awesome problem of getting good information in advance so that you can size up the scene you know with some certainty you can actually get in on a British air fare or package tour bargain.

Thanks to an agreement among the international scheduled airlines, it's "illegal" to reveal foreign discount fares in this country. Thus you're not even supposed to hear about such plans as "infant" fares that are sold out of London no earlier than 21 hours before you want to leave for such places as Paris, Brussels and Amsterdam, and which reward you with a discount of roughly 42 percent if you also meet a few other length-of-stay requirements. Nor would you normally be able to learn that, say, Johannesburg in South Africa is available on an advance purchase excusion (APEX) fare that, combined with a cheap flight to London, could save hundreds of dollars over a U.S. APEX fare.

Even more irritating is the fact that it's also hard to do business by mail. Few British travel agents and tour operators will take on the additional burden of overseas correspondence, and although a number of British tour companies are now represented in this country, that doesn't mean you can get anything close to the full picture of what's in London's "bargain bins." (Two companies are Cosmos, 69-15 Austin St., Forest Hills, N.Y. 11375; and Thomson, M.S. Marketing Services, Ltd., 516 5th Ave., New York 10036.)

For tour buyers the "bins" hold a full load of good news-bad news. To say flatly, as some have, that you can buy "comparable" tour packages for "much less" in Britain than you can in the United States is, in a word, baloney. A few, sure. Most, no. What you can buy easily are tours that are cheaper because they offer less, notably in the quality of accommodations and foods. Few U.S. tour operators have seen any profit in offering truly rock-bottom-priced tours, so they haven't. By the same token, for people with only so much money to spend, they're often "just what we've been looking for!"

My own view is that I wouldn't seriously consider any package that includes meals. I have no faith in tour operators meeting my tastes or standards.

I would further discard any tour that involved lots of touring - scheduled sightseeing and other planned activities, that is - because I prefer the sense of discovery I get going on my own. Obviously, though, a loaded package is what lots of travelers love, and they can find examples in London at virtually any price, from as little as an incredible $5 a day plus air fare for a few very thin ones, on up for thicker ones.

Some of the lowest-priced tours are currently offered by London tour operators who deal directly with the public without going through travel agents. Causing considerable commotion this winter is the arrival on the London scene of one of the biggest of these direct dealers, the Danish firm of Tjaereborg. British agents already were unhappy with the presence of home-grown direct dealers like Martin Rooks and Saga Holidays (this one specializing in cheap, long-stay packages for senior citizens), but the public has apparently found their company worth keeping. Martin Rooks, for one, often has long lines outside its main office.

For air fare bargain hunters, the story is similar. The British ae currently a new game that involves "one pound" tour packages. (You go to a travel agent and sign over accommodations you've supposedly arranged for yourself in a given city. Then they're sold back to you for one pound - approximately $2. You've then made yourself eligible for a great discounted air fare to the designated city.)

Laker Airlines, for instance, has round-trip London-Tunisia budget fares for approximately $112; London-Vienna, $90. Thomas Cook has Fare Share seats to Rome for about $62, which, it should be noted, is almost $340 less than the normal London-Rome economy round-trip fare. It should also be noted that the awesomely high economy fares are what people have to pay if they're bad shoppers or for any of many other reasons can't or don't get in on a discount arrangement.

It's hard not to look longingly across the waters, though, when you find out that the British have charters and advance-purchase excursions to all sorts of destinations we don't. There are even some one-way APEX fares to places such as Bangkok and Singapore. Some are on appealingly frequent schedules as well.

Nairobi, Kenya, for instance, doesn't inspire everyday cheap flights from New York (much less from anywhere else in the United States), but there's service from London and the price isn't half bad either. A "club" called Wexas recently was advertising seats from London for approximately $430 round trip (and offers to do business by mail: write 45 Brompton Road, Knightsbridge, London SW3, for details). The cheapest New York-Nairobi excursion fare is $1,176. (There were some U.S. charter tour bargains from Boston, New York or Washington to Kenya and Tanzania, but the trips were cancelled because those countries closed their common border in a dispute.)

In the London market, you'll also find student fares (for full-time students up to the age of 30) and youth fares ("youths" up to 22 most of the time, 26 some of the time, depending on the destination). Lately, though, these often have been more expensive than the one-pound tours and various offerings from "bucket shops" - unacredited travel agencies that sell cut-price air tickets passed on to them by "wholesalers" and airlines.

The one-pounders, in fact, were invented to bypass the bucket shops and nudge them right out of business. However, the gray market still appears to be thriving - in Amsterdam, Brussels, Rome, Bangkok, Singapore and Hong Kong as well as London. Many are regular newspaper advertisers quire reliable.

Just for testing purposes, I marched up to a charter airline desk at London's Gatwick Airport a few weeks ago and said, "I suppose it's too late to book an air-only seat this week?"

The agent on duty gave me a level look. "WE can't sell you a seat," she said. "If you looked in the newspaper though . . ."

I guess that's the bottom line on the London scene in general: "If." If you can garner the information you need from London publications, friends or travel agents; if you have the time, and if you're up to living with uncertainty - yes, you may find that for travelers, London's grass is sometimes greener.

In the process, you might also begin to wonder why so many airlines go on and on about the fearful upsets that industry deregulation might bring. In many parts of the world, they clearly deregulate at their own convenience, and the only people demonstrably suffering are price-dependent shoppers who still haven't learned how thenew games are played.