The British invade the Wild West - to teach acting and to perform.

On the cover of the program is a painting by R. C. Gorman of a statuesque Pueblo Indian woman, her severe and regal profile turned upward; draping her entire form is the bold red, white, and blue design of the Union Jack. It's at once a stirring and an amusing image, and it well conveys the excitement of having top-flight British actors performing and coaching drama students in such an un-British place as Santa Fe.

The program was for a performance of Willie Russell's popular comedy ''Educating Rita,'' which ran in Santa Fe in mid-July. Responsible for this production was a three-year-old organization called the British American Theatre Institute, or BATI, the brainchild of New York theater and television producers Albert W. Selden and Ralph Levy, both now residents of Santa Fe.

The fact that ''Educating Rita'' and its sister production, Harold Pinter's ''Betrayal,'' came to New Mexico from the Redgrave Theatre in Farnham, Surrey, England, is characteristic of the enthusiasm for the arts and willingness to support them pervading this ancient Southwestern city.

The idea behind the BATI program is to provide college students with an opportunity to learn about acting from professional British actors, both by attending classes they teach and by watching the actors' performances. The world-class status of British actors, as well as their reputation for an expert style with a strong emphasis on technique, means they have a lot to offer students.

To avoid immigration problems or protests from Actors' Equity, the US theatrical union, the five British actors entered the United States on teaching, rather than acting, visas. And to keep BATI's financial outlay as low as possible, the two productions had casts of only two and three, respectively.

Judging from the reviews of ''Educating Rita,'' these visiting actors have provided top-quality theater, the likes of which any city would be proud to support. The audience could have imagined itself in London or New York, where this intelligent and funny play enjoyed great success a few seasons back. Even the broad North Country accent of the leading lady, Melanie Hill, was in no way watered down for a ''provincial'' American audience.

Over enchiladas at the La Fonda Hotel in Santa Fe, Ralph Levy and Albert Selden chatted about their organization.

''I moved out here just a couple of years ago from New York,'' Mr. Selden explained. ''I'd been working on Broadway, but it's getting so expensive (to produce plays there that) it's not fun anymore. When I came out here I knew I didn't want to do nothing. I knew that if there was some theater around, I'd want to get involved, but without any of the high-pressure nonsense, and it's proved to be a great deal of fun.''

The BATI programs are run on the premises of local colleges - the University of New Mexico in Albuquerque and the College of Santa Fe - and although their summer courses are for university credits, they're not actually a part of the college curricula.

Mr. Selden continued, ''It's a special school, and we help pay for the school by having the faculty perform.

''We made this very lucky connection with the Redgrave Theatre - we think it's very lucky, because they're thrilled to come here. They like what they're doing and we like working with them. They're marvelously talented and understanding of their American pupils.''

The Redgrave Theatre of Farnham, a little more than an hour southwest of London, was renamed in 1972 for Sir Michael Redgrave, the actor, and his children, but it has existed since 1939. Of the five actors who came to New Mexico, all have impressive credits and three are graduates of London's famous Royal Academy of Dramatic Arts. They all expressed great enthusiasm and delight on finding themselves performing and teaching in such (to them) exotic places as Albuquerque and Santa Fe.

The cast of ''Betrayal'' had worked together before as a group called Albion (a poetic name for England). As one of their members, Anthony Naylor, explained, the group was formed ''because we like to eat.'' Acting opportunities in England were just too scarce, so they decided to create their own company. Then they were hired as part of the Redgrave Theatre and asked to bring their production of ''Betrayal,'' directed by Redgrave artistic director Stephen Barry, to New Mexico.

BATI plans to have the Albion group return to America with ''Betrayal'' next January to tour a number of colleges in the West and Midwest - where the organization hopes to recruit students for future summer sessions.

I had an opportunity to talk with Melanie Hill, from the cast of ''Educating Rita,'' after one of her workshops with students. ''The reaction of audiences here has been overwhelming,'' she said. ''But I've got more from teaching than from the applause for doing the show.''

And how did she like working in the Wild West? Melanie Hill tossed her mane of copper-colored hair and grinned. ''I love it here. I liked Albuquerque, I like everything. Me jaw is still on me knees.''