Peter Allen writes songs and they become travel agency anthems.

There was "I Go to Rio," his own first hit. "I've been to Rio twice," Allen says between bites of a mid-afternoon lunch before his concert at Wolf Trap last night. "I was invited after I wrote the song. It's like 'White Christmas' down there, they kind of drag it out at each carnaval.

There was "Bi-Coastal," a song that actually preceded the cliche'; written about people who commute endlessly between L.A. and N.Y.

There was "I Still Call Australia Home," an Aussie "Country Roads," which "kids always sing at Christmas. And Qantas plays it as you fly into Sydney."

Peter Allen, the bon vivant with the bon mots, is one of Australia's top pop exports, not yet as marketable as Olivia Newton-John or AC/DC, but certainly in for a longer run than the assured Helen Reddy. In fact, he's been designated as an ambassador at large. "My duty is to be a nice Australian," he says brightly. "Which is basically to stay out of jail and keep saying I'm an Australian."

Someday, Allen may even get around to writing a song called "Bi-Continental," since he still spends three months of the year down under. But his career has been breaking stateside in the last few years, first through his songs for other people ("I Honestly Love You" for Olivia Newton-John, "I'd Rather Leave While I'm in Love" for Rita Coolidge and "Don't Cry Out Loud" for Melissa Manchester) and then with increasingly flamboyant shows that propelled him from tiny New York cabarets to a sold-out, week-long run at Radio City Music Hall last year. Wolf Trap was the end of a summer tour; now the rehearsals start for another extended run at the Music Hall in September.

Not bad for a young singer who was plucked almost 20 years ago from a Hong Kong Hilton by none other than Judy Garland. Allen had been half a duo at the time ("we were pretty crummy") when Garland, after a disastrous tour of Australia, heard him. "I barely knew who she was," he recalled. "And I got to know her as a friend before I ever saw her work. The Australian press had killed her, and then she'd gotten real sick in Hong Kong."

Garland was a victim of Australia's cultural insecurity, according to Allen. "It used to be dreadful 15 years ago. The Australian press were all ex-police reporters and they were known as celebrity baiters, especially if the celebrities were American. They would get a hotel room next door and drill holes in the bathroom walls and photograph you on the toilet! It was a nightmare; they're all right now."

Until recent years, Australian music tended to be dominated by English or American styles and Allen started off with "Little Richard songs, Elvis Presley, the Everly Brothers, Neil Sedaka." He was, even then, flamboyant, though "when you're 15 you don't realize that you're 'flamboyant.' But when I started out, I was standing up at the piano, kicking my legs up because that's what piano players did then. I've gone back to it in my middle years he's 38 , which is why it looks weird now, but that's what I did to start off."

He and then-partner Chris Bell worked with Garland for three years, but he got a little closer to home by marrying Garland's daughter, Liza Minnelli. The marriage lasted seven years. "We don't see each other very much," Allen says of Minnelli, though he did coauthor the theme of her recent film, "Arthur." "She's been married twice since me and her latest husband's not toocrazy about me," he grumbles.

Invaluable lessons were gained from both mother and daughter, however. "Having worked with Judy, you could see just how bad everyone else is on stage. It makes you try to keep yourself honest on stage, to give some kind of value for money, to let people in on something in your performance, something that's almost gone out of style. She set a standard that was very hard to meet."

Minnelli was the one who encouraged Allen to start writing his own songs, including a fine tribute to Garland, "Quiet Please, There's a Lady on Stage." His songs have been hits for Judy Collins, Frank Sinatra, Patti LaBelle and Dionne Warwick. Director Bob Fosse used "Everything Old Is New" in "All That Jazz" and the two will be collaborating on a new Broadway musical, "Big Deal," as soon as Fosse is finished filming a biographical movie about Dorothy Stratten. "He's like me in that he can only work on one thing at a time; when he finishes we'll go back to work on the show," says Allen, who already has four songs in the can.

He's also written and performed the theme for the upcoming film about Coco Chanel, "Chanel Solitaire" ("a terrible movie but a pretty theme") and may surprise his fans as the Pirate King in a D'Oyly Carte "Pirates of Penzance" scheduled for television this fall. The production was part of a special project to save the financially troubled London company by videotaping 12 different Gilbert & Sullivan works for sales. "They didn't want the D'Oyly Carte to collapse and not have a record." As written, that version was "very severe, couldn't change a beat, couldn't change a breath," according to Allen. "I think they'll faint in London when they see the film version of the Broadway show. But even though I'd never acted, I had a great time."

Allen is already looking forward to going back to Radio City Music Hall. On his first visit, he became the first outsider since Ann-Margret to dance in the Rockettes line. "I was the first male," he says proudly; he also became the first male Honorary Rockette. The show may not be as flashy as last year, when Allen rode in on a rent-a-camel leftover from a Nativity play. "I've cut back on the gimmicks. Otherwise it was going to turn into a circus. It's a dead end, you end up like Bette Midler did in New York: If you have King Kong in the first act, what do you put in the second act? When things get in the way of the person on stage, you're in trouble, so I just relaxed and let the songs take care of themselves . . . and people have reacted just great."

And, he points out, those people are pretty regular people, as opposed to the "gay cult" he had early in his stateside career. "Frances Faye, who started me off in Australia as an opening act, was always real 'real' and honest and brilliantly funny . . . and 20 years ahead of her time. She got cursed with the gay image and nobody would book her. And Bette Midler is practically doing her act and I'm practically doing her act and it'll be because of those elements that people now find it interesting."