It sounds like a good plan. With credit cards maxed out, Colin Wilson will set off in his canoe and never come back. Once he is presumed dead, his wife, Deborah, will claim the life insurance. Pension and mortgage payouts will follow. Meanwhile, Colin will go into hiding until they can make a fresh start.

A marriage capsized … Sarah Belcher and Phil Corbitt in All at Sea. Photograph: Von Fox Promotions

Inspired by the true story of “canoe man” John Darwin, Alison Carr’s two-hander looks as though it will head into the sitcom territory of Can You Keep a Secret? Like that BBC comedy, in which Mark Heap does a bad job at hiding, All at Sea considers the hurdles of staying out of sight. Where to go if someone comes around? What if the phone rings and you accidentally answer? How to stay sane?

But unlike that show, Carr plays it for drama, not laughs. The further we go into Maria Crocker’s production, the more the challenges are not just practical but psychological. At first, this is primarily to do with Colin’s life in limbo. Played by Phil Corbitt, he is the captain relegated to the subs bench, at once controlling and ineffectual. It drives him to distraction.

But the real intrigue is what happens to Deborah. Played by Sarah Belcher, she remains engaged with the world. Having gone through the motions of grieving, she finds herself living an emotionally independent life. It is as if Colin really were dead.

While nothing changes in the prison of their home – in a functional if too literal design by Hannah Sibai – things continue to evolve for Deborah: the people she meets, the clothes she wears, the self-worth she feels. Slowly, subtly, the man she loved looks ever more patronising, jealously keeping her in check.

Corbitt and Belcher are excellent at the push-pull of contradictory emotions, their troubling chemistry making the play’s grisly conclusion feel necessary.

• At Live theatre, Newcastle, until 10 October and at Stephen Joseph theatre, Scarborough, 16–31 October