I'm looking for the name of a book published about 20-25 years ago. A
man  advertised in the London papers for a woman to live with him for
a year on a desert island.  The woman he selected wrote the book and I
believe the word "island" was in the title.  A few years later he
wrote a book with his side of the story.

The man who placed the ad was Gerald Kingsland. The woman who accepted
the offer was Lucy Irvine. Her book about the ensuing adventure was
"Castaway," and his was "The Islander."

"Lucy Irvine replied to an advertisement which simply said: 'Writer
seeks "wife" for a year on a tropical island.' Most of us would have
probably thought about how wonderful it would be to get away for a
year, to peace and quiet away from the hassles of everyday life. We
would have sighed a little and then forgotten all about it. But not
Irvine. She wrote to Gerald Kingsland, the author in the ad, and
before she had time to think about it she was leaving her life as a
clerk with the Inland Revenue far behind as she headed off with her
new 'husband' to a tropical island somewhere between Northern
Australia and Papua New Guinea."

Amazon.co.uk: Castaway
http://www.amazon.co.uk/exec/obidos/ASIN/0552146811

"He was a successful journalist and publisher in England, then a wine
grower in Italy. In the wake of a severe personal crisis, Kingsland
set out to become a modern Robinson Crusoe; he sought a remote
tropical island where he could be self-sufficient, as well as a
suitable companion (young, female and willing). Neither requirement
was easy to find. Kingsland tried three islands in seven years and
selected his companions by advertising in newspapers. First, there was
Cocos Island, in the mid-Pacific, his three young sons joined him
there for a time. With a 21-year-old 'GirlFriday' he went to Robinson
Crusoe Island off the coast of Chile, trying without success to reach
Selkirk Island. On the third try, Kingsland advertised for a wife and
drew Lucy Irvine, age 24. They went to Tuin, in the Torres Strait
between Australia and Papua New Guinea, uninhabited and lacking a
dependable water supply. Theirs was a tempestuous relationship (Irvine
published her version of life on Tuin in Castaway; they nearly
perished, but were saved by Badu Islanders. If there is a moral to
this rollicking tale, it is that a Crusoe-type existence is
improbable."

Amazon.com: The Islander
http://www.amazon.com/gp/product/0450058530

"Castaway" was adapted into a movie, with Oliver Reed as Gerald and
Amanda Donohoe as Lucy:

Internet Movie Database: Castaway
http://imdb.com/title/tt0092732/

My Google search strategy:

Google Web Search: "gerald kingsland" island
://www.google.com/search?hl=en&q=%22gerald+kingsland%22+island

I hope this is precisely what you need! If these are not the correct
books, or if anything is unclear or incomplete, please request
clarification; I'll gladly offer further assistance before you rate my
answer.

Best regards,
pinkfreud

That's the book!  Thanks for the quick answer.

Thank you for the five stars and the nice tip!

~pinkfreud