“What is growing up, precisely?” That’s an unusually loaded question since it’s asked by the woman who inspired “Alice in Wonderland” of the man who inspired “Peter Pan.” Having issued the challenge, Judi Dench’s Alice and Ben Whishaw’s Peter then proceed to compare how their dominant — and possibly detrimental — gilded childhoods shaped their lives. Although John Logan’s speculative new play brims with ideas illustrated by Michael Grandage’s handsomely designed London production, its lack of a motor means that only at the very end does it deliver on its intriguing premise.

Although his protagonists are known to have met just once in a bookshop prior to a Lewis Carroll centenary exhibition in 1932, Logan has free rein. Nothing is known about what the two of them said to each other.

His invention starts with wary formality between them. Thirtysomething Peter attempts to disguise his nervousness while the 80-year-old Alice presents surface high status. But Peter’s dismissal of Alice’s easily trotted-out, idealized version of what Carroll’s fiction did for her own life — “I feel I was given a gift” — leads both to reconsider. Christopher Oram’s dusty bookshop backroom flies out to reveal a gaily colored toy theater of their imagination.

Between them, they conjure up not only their respective authors Carroll (Nicholas Farrell) and J.M. Barrie (Derek Riddell) but their fictional selves. Olly Alexander darts about as bright-eyed, sharp-edged Peter with Ruby Bentall’s self-composed Alice in Wonderland forever trapped in the iconic dress supplied by Tenniel’s original illustration.

At its best, this art/life animation of figures in a landscape transcends its echo of Sondheim’s “Sunday in the Park With George.” It rings particularly true that while Peter and Alice can interrogate each other’s version of their past, they find it far harder to square up to their own demons. Both of them deal in denial and the play consists of them peeling back layers of it.

Lurking behind what Carroll described as the “golden gleam” of idealized memory are inchoate desire and the death of innocence. It’s to Logan’s credit that as they each face up to the dangerously mixed motives of the men who shaped them, there is no easy revelation of a single unified “truth.” Mercifully, the play refuses an overly neat conclusion about how one should deal with a painful past and grow up.

There is, however, no imperative or urgency to the encounter. Using the potency of these fabled childhoods as a framework, Logan is examining erotic obsession and its suppression, self-determination, the consolations and casualties of fantasy and more. But without gathering momentum to hold the audience, it becomes a fantasia on themes rather than a developing drama. There are touching moments — death stalks both Peter and Alice’s lives — but too much is patiently explained. Subtext is replaced by hints of withheld information, the uncovering of which feels predictable.

Initially amusingly impervious, Dench deftly shows Alice using shrewdness as a defense. Released into the world of memory, she effortlessly suggests girlhood and, best of all, listens like a hawk. So too does hangdog Whishaw, his arms awkwardly clamped to his thin frame, his hands neurotically scrabbling in his dowdy jacket pockets. His eyes darting about, he looks exhausted and victimized by his past, an affecting contrast to Dench’s Alice who steers a path through life’s difficulties to self-acceptance.

The nostalgic Victorian world created by the design team is highly evocative. At the end of the penultimate scene, hard-won adulthood returns as the childhood landscape is replaced by the lowering return of the dowdy bookshop set. The effect of childhood disappearing is unexpectedly moving, but that physical image underlines the feeling that the evening is theatrical rather than dramatic.

Peter and Alice

Noel Coward Theater, London; 946 seats; £57.50 ($87) top

A Michael Grandage Company presentation of a play in one act by John Logan. Directed by Michael Grandage.

Sets and costumes, Christopher Oram; lighting, Paule Constable; sound and music, Adam Cork; production stage manager, Sophie Gabszewicz. Opened, reviewed March 25, 2013. Running time: 1 HOUR, 25 MIN.

With Ben Whishaw,  Judi Dench, Nicholas Farrell, Derek Riddell, Olly Alexander, Ruby Bentall,  Stefano Braschi.