To Nina Bawden, the term "written to order" seems to mean written at the request of a particular person for his or her enjoyment or benefit.
But in the nonfiction publishing industry, at least, many books published are written in response to contracts drawn up between individual authors and particular publishers. The publisher solicits manuscripts on specified subjects from authors whose work the publisher is already familiar with. The author agrees to write the book, the parties sign a contract to produce it, and the book is scheduled for publication in the publisher's next lineup of titles. This would seem to describe an industry in which a great many books are written to specification or, in other words, "to order."
In fact, mainstream publishing houses so rarely accept and publish unsolicited manuscripts that people in the publishing industry have given them a special (and not terribly flattering) name: over-the-transom manuscripts. Albert Greco, The Book Publishing Industry (2013) explains:
Over the Transom
A small number of manuscripts get published each year because they were submitted "over the transom" (i.e., sent unsolicited to a publishing firm with a "To Whom It May Concern" letter). This approach is done without the benefit of a sponsor (e.g., an agent, an author published by the firm, another editor, an academic advisor, etc.). Whenever a book firm receives a manuscript over the transom, it is relegated to the "slush" pile; in 2012, most large New York publishing firms receive well in excess of 100–150 over-the-transom manuscripts each week. How many of them ever get published?
Although no one keeps tabs on this type of submission, The New York Times once commented that the odds of this type of manuscript being published were 15,000 to 1. So the odds of a manuscript sent cold to a commercial publisher ever getting into print are, at best, remote. For example, J.K. Rowling was rejected by almost every trade house before Scholastic took a sample of an unknown author. Among university presses, the rejection rate for over-the-transom manuscripts is almost certainly higher.
Especially in nonfiction books, where the credibility of the author with regard to the factual information presented in the manuscript is crucial, it is highly unlikely that an unknown author will be approved for publication just because the person's writing is good.
So it may be true that Nina Bawden never wrote a book "to order"—and it seems quite likely that she is an excellent author—but it also seems likely that she never submitted more than one book over the transom and had it accepted for publication. In fact, her Wikipedia page indicates that her literary career closely tracks her marriage to Austen Kark, described as "a reporter who eventually rose to managing director of the BBC World Service." When you're trying to get started as an author, it helps to have a booster who is successful—or at least knows people—in an allied industry.