Budget Bus Service From London to Edinburgh : ‘Slow Coach’ stops at hostels on a circuit that also includes Bath, Cambridge and York.

A budget-priced bus service geared to backpacking travelers is now available in Britain.

The Slow Coach starts in London and, traveling clockwise, continues on to Windsor, Bath, Stratford-upon-Avon, the Lake District, Edinburgh, York and Cambridge before returning to London.

The buses will pick up and drop off passengers at local youth hostels in each destination. Passengers can get off and stay as long as they want. The company has four buses, which stop at each hostel four times a week.

There are no age restrictions on using the service, but you can expect that the bulk of the passengers will be young backpackers. A ticket to travel the full 927 miles, round trip from London, costs about $110. Ticket-holders have up to two months to complete the route. The tickets are transferable, so it is possible to change your plans and resell the unused portion of your ticket.

It’s also possible to purchase tickets to travel only specific portions of the route. For example, London to Windsor costs about $5; London to Stratford is about $25; London to Edinburgh, about $65, and London to York about $90.

Tickets for the Slow Coach are on sale at British YHA youth hostels along the route, and at YHA Travel at 14 Southampton St., London, in the Covent Garden area.

Ticket-holders who plan to use hostels along the route during the busy summer season are encouraged to use the “Book A Bed Ahead” service available for key British hostels. There is a fee of 1 (about $1.60) for the reservation service, and you are asked to make a 5 ($8) deposit toward the overnight fee. The nightly rate for dormitory accommodation ranges from about $12 to $20.

You can arrange to book a bed ahead at participating British hostels and at YHA Travel.

While you are in London, you’ll find that single-fare subway journeys can be pricey. I found the average cost of a trip in central London was about $1.50. If you plan to use the system often, invest in a London Transport One Day Travelcard. It’s valid for unlimited travel on the underground and buses (not the night buses, however) within specified zones. You can begin using it at 9:30 a.m. on weekdays, or anytime on weekends and holidays.

The Travelcards are priced according to the size of the zone in which you wish to travel. A one-day Travelcard valid for unlimited travel in central London costs about $4.

The Travelcards can be purchased at London underground ticket offices and self-service machines in the stations. Weekly and monthly cards are also available; however, for these you must supply two passport-size photographs.

If you plan to move on from London to Europe, you’ll find that a variety of travel agencies are geared to budget travelers and can arrange special deals for young travelers.

For example, Campus Travel, which is owned by the Irish Student Travel Service, and which also has an office at 14 Southampton St. in London’s Covent Garden, is one of a number of travel bureaus that sell special Eurotrain Explorer tickets.

Here are some of the fares now available from London:

* The Paris Explorer, which is valid on a route from London to Rouen, Paris, Brussels, Brugge and back to London, costs about $125.

* The Capital Explorer: London to Paris, Brussels, Amsterdam and back for about $140.

* The Dutch Explorer: London to Amsterdam, Brussels, Brugge and back for about $110.

* The Rome Explorer: London to Paris, Pisa, Rome, Florence, Lucerne, Strasbourg, Luxembourg, Brussels and back for about $280.

* The Eastern Explorer: London to Amsterdam, Berlin, Prague, Budapest, Vienna, Zurich, Brussels and back for about $290.

* The Riviera Explorer: London to Paris, Nice, Pisa, Rome, Florence, Basel, Luxembourg, Brussels and back for about $285.