LONDON. Mastering the art of traveling together...father and daughter share the outrageous and the traditional

WHAT do you do when a teen-ager sees her first trip to London -- indeed her first trip abroad -- solely as a shopping spree? When the prospect of Buckingham Palace, Kensington Gardens, Trafalgar Square, and Westminster Abbey pales next to the attractions of boutiques on the King's Road and Carnaby Street, and glimpses of ``skinheads'' dressed in black leather and chains? Julie Wickware's father was faced with such a dilemma recently, and after considerable soul-searching and a creative effort at mutual compromise, he and his daughter came up with a solution that suited them both.

``I was not going to take her to London just to buy clothes,'' recalls Julie's father, Dana Wickware, of Greenwich, Conn. ``She would have to spend at least part of the time with me in museums and in seeing the city. My feeling was that even if she didn't seem interested in these things now, she would remember them later. I simply wasn't going to let her waste this opportunity.''

Both father and daughter -- a sophomore in high school -- soon discovered that there were unexpected things for Julie to enjoy right where she thought there was nothing to interest her. While her dad queued up for theater tickets in Leicester Square, Julie browsed among the post card and souvenir vendors, buying pictures of punks with Mohawk hairdos to send home to her friends, and lapel buttons with messages like ``Relax.''

In the National Gallery, Mr. Wickware marveled at his first viewing of masterpieces such as Van Eyck's ``Betrothal of the Arnolfini,'' and he made a point of showing it to Julie. But she seemed less than enchanted, gazing glumly at something she felt little inclination to admire simply because she was ``supposed to.''

That is not to say that she did not have her own preferences in painting. She responded particularly to Canaletto's Venetian scenes.

``I liked them because it was amazing to think people could still go there today,'' she recalls. ``It looked like something that couldn't exist, and yet I knew it still did.''

Since their stay in London was short, Mr. Wickware had planned a full day for visiting the city's two historic churches, St. Paul's Cathedral and Westminster Abbey. But he was well aware that so many hours of contemplating baroque arches, illustrious tombs, and barrel vaults would be tedious for his daughter. On the other hand, he wanted her to see them, if only briefly. She wanted to spend the day on the King's Road, shopping and getting her hair dyed pink.

The solution consisted of a little of both. After carefully consulting street maps and bus routes, Julie and her father agreed that she would go with him in the morning to St. Paul's, stay there for an hour, and then proceed by herself to the King's Road, halfway across London and two bus rides away. He would then go to Westminster Abbey after lunch. Julie agreed to meet him there at 3 p.m., in time to spend an hour in that church, too.

``Culture is all very well,'' says Julie's father. ``But I wanted to let her be a kid, too. I wanted to make it possible for her to do the things she wanted to do. When I was sure it would be safe for her to travel around London by herself, it seemed like a good opportunity for her to feel a bit of independence, to have a bit of an adventure on her own.''

The scheme worked without a hitch. Even though she was 20 minutes late finding her way back to Westminster Abbey (``My haircut took forever, and I had to take a cab''), her dad wasn't unduly concerned. ``I trust her,'' he explained. ``And when she appeared with a bright pink forelock, I must admit she looked very fetching.''

Of all European cities, London is perhaps the most fun for an American teen-ager to visit. Not only is there no language barrier, but the fact that London is today's undisputed capital of punk makes it especially appealing to the young. Julie got a kick out of just seeing other youngsters on the streets, many of whom had hairdos and outfits that were far more outlandish than those she sees back home. And her father made a point of taking her to restaurants and theatrical performances she would enjoy.

Julie had read about London before the trip, too. She knew where the shops were that she wanted to visit; she knew she wanted to eat at Hard Rock, a flamboyant hamburger restaurant off Hyde Park Corner that has recently opened a branch in New York.

Although her father wanted to attend a performance of the Royal Shakespeare Company or the National Theatre, he also made a special concession and took Julie to see ``Little Shop of Horrors,'' a rock musical imported from New York.

``It was fun,'' he recalls. ``Outrageous. I think I enjoyed it as much as she did.''

By the time the trip was over, both father and daughter were thoroughly satisfied with their experience. Mr. Wickware's appetite was whetted for more extensive visits in the future, and Julie took home more than the pointed black boots, electric green socks, drop crystal earrings, and outsized T-shirts she had purchased.

``I had a great time,'' says Julie. ``I had heard so much about England and I liked getting to see it myself. And now it's good because a lot of my friends have been there and I can talk to them about it.''