"Most expensive city in the world for tourists," announced the headline in a recent British newspaper. The article went on the describe how Mr. and Mrs. X, two vistors staying in a firstclass hotel, managed to spend in one day ("without really trying") a total of 133 pounds -- or $307!

Sir Henry Marking, chief of the British Tourist Board Authority, attacked the report in the Financial Times, pointing out that it was based on only five international hotels catering to expense-account vistors out of a total of 1,300 hotels in the British capital.

That is true, though the fact remains that London today is far from the bargain it used to be -- which is also ture of the other major cities in the world.

But there's still hope for the budget traveler. Remember Arthur Frommer? A long time ago he wrote a book titled "Europe on $5 a Day." Now he's offering "London Without Cash." It's not a free trip, but with the name of a unique package tour program.

The "London Without Cash" brochure says that you can leave your wallet at home, because everything -- absolutely everything -- is included and prepaid. For $399 a person, based on double occupance (plus $478 for roundtrip air fare from Chicago) I got seven nights' lodging, all meals, unlimited in-city transportation, a dinner show at an Elizabethan-style nightclub with all the wine and beer I wanted, four theater and two movie tickets, a sightseeing pass and airport transfers. Taxes and tips are taken care of, and these extras are thrown in -- two cocktails on the plane, a morning newspaper, prestamped postcards and even a nightcap each evening.

(The tour price rises to $499 on April for the summer "high" season ending Oct. 31, to cover higher land costs -- it is guaranteed by Frommer to remain at that level as long as the pound hovers around $2.40, according to the packager. Airfare will vary, depending upon the city you take off from and the rate in effect for the season during which you fly. Cooperating airline is British Airways.)

Forget your American Express card; you can leave home without it. "You needn't spend a single extra cent in Londoon," the brocure says.

It's a boast that sound almost too good to be true, one that should be checked out -- so this writer did just that.

Does "London Without Cash" pay off?

Yes, you can leave your wallet at home.

After taking the one-week package and testing all its facets, it can be reported that it does deliver. It's a budget vacation -- transportion in buses and subways instead of taxis, accommodations in a touris-class hotel -- but it's spiced with some elements of luxury -- excellent theater seats, and two dinners at delux restaurants.

The experience showed why this type of prepaid package may well be the wave of the future in tourism. As the price of travel skyrockets, it's reassuring to know you won't have any financial surprises on vacation in a foreign land. It's also a pleasure to avoid hassles with handling the figuring out the value of foreign currency. Tipping, another worry, also is eliminated in such a tour.

This traveler spent a week in London in January, received all the advertised elements of the tour, and had to spend only five British pence (about 11 cents) to make a phone call for a reservation for the Elizabethan banquet.

In addition to eliminating money worries, the plan provides a savings of more than $100 a person over the cost of buying the same vacation on your own.

Here's how the tour works. First of all, it's not really a tour in the group sense. You have the freedom of doing it all on your own, at your own pace. You're not attached to a group at any time. It amounts to independent travel at money-saving group rates.

After making your reservation at a travel agency (at least three weeks in advance) and paying for the package, you receive a packet containing an airline ticket (British Airways) and 13 vouchers that you exchange along the way for various parts of the package.

In every case -- whether at the hotel, a restraunt or elsewhere -- the vouchers were accepted without question.

One small problem arose twice at restaurants. The vouchers state: "This cheque entitles the holder to a three-course meal of their choice from the a la carte menu. It covers the cost of coffee, service and VAT (tax) on this meal." Twice, though, waitresses tried to get an extra tip. They said the vouchers don't include service, which they plainly do. Just show them the fine print.

The tour's meal plan is one of its strengths. In your seven-night stay you'll eat 21 meals -- seven continental breakfasts at your hotel, five lunches in pubs and two at a hotel "carvery" restaurant, six "Eat Like a King" dinners and the Elizabethan banquet.

You have a choice of about 50 london restaurants where you can order anything on the menu -- even caviar or the most expensive steaks. It's nice to look at a menu and not feel you have to hold yourself to a certain budget.

On the negative side, being limited to 50 restraunts does restrict your range of choices, but Frommer is planning to expand the list substantially.

One pitfall should be pointed out. There are some who will be tempted to order wine with dinner. It's not included in the voucher, so you'll have to fork over some cash. The cheapest house wine at most places costs about $5 for a half bottle.

You're allotted 10 one-pound vouchers for use at some 50 Chef and Brewer pubs throughout London. That figures out to two pounds a day ($4.50) for lunch, more than enough to stuff yourself and satisfy your thirst with the excellent British beer. The only hitch is that you are not given change if your tab happens to be less than two pounds.

Since you're on your own, you have to be your own tour director. That calls for some careful planning to coordinate the right timing of sightseeing, meals, theater, etc. The job is made easier by Formmer's 250-pate "Guide to London" and especially by the street listing seven suggested daily itineraries. These are given to you on arrival.

For maximum enjoyment you should rough out your sighseeing strategy for the week on the first day. That way you won't come to the end of the week and be disappointed you didn't see a certain attraction.

Your evening entertainment requires planning, too. If you're going to the theater that night, you should select a restaurant reasonably close (in transportation time) to the theater. Since the curtain time is 8 p.m., you'll have to be at the restaurant by at least 6:30 or risk indigestion in the rush to eat fast and make the show.

You get four preselected theater tickets -- usually a mix of two musicals, a comedy and a drama. If you don't like the selecteon, you can trade at the downtown Frommer office or the Frommer desk in your hotel. Currently, there are about 36 stage shows running in London. Frommer gives you some tickets and some vouchers for tickets. The vouchers must be exchanged for tickets at the theater a half-hour before the curtain.

A final word of advice: Bring a litle cash, even though you don't have to. You're bond to want to buy a souvenir of two, maybe a T-shirt with a map of the Underground on it ($7) or a toy double-decker bus ($4).

Also, any visit to London should include a stop at Harrod's, Europe's largest department store. Who can resit making at least one tiny purchase? After all, china, glassware and some clothing items are still good buys.