There are so many plays about the end of the affair that it is a pleasure to see one about the very start – especially when that play is as honest, funny and good-hearted as David Eldridge's Beginning.

Sam Troughton and Justine Mitchell play – beautifully - Danny and Laura, an odd couple who are left alone at the end of her house-warming party. Amidst the wreckage, the tattered streamers and the empty bottles conjured on Fly Davis's sharply observed set, they make the first tentative steps towards a relationship.

More accurately, Laura makes the seductive moves while Danny, who admits he has "no radar", more or less consistently puts his foot in it, shuffling his weight and fiddling with his beer bottle, as long, awkward silences punctuate the conversation. Over the next hour and forty minutes, as the clock on the wall marks their progress in real time, they attempt to climb through their embarrassment and their difference, finding mutual ground in Strictly and Scotch eggs, falling over the hurdles of relative wealth and class, trying to make warm, human links.

Their fumbling efforts are incredibly funny but sometimes so truthful they're almost too painful to watch. The moment when she says 'kiss me' and he whips out a bin bag to tidy up, sooner than face her demands, and the protracted scene in which they dance together, are so vividly observed that they make you squirm in your seat.

Underneath the detail is a great, aching study of loneliness and the ways in which the internet and the pleasures of Facebook have made modern dating an even more perilous minefield. Laura believes she knows Danny because she can look him in the eye and judge his face; he is more comfortable with internet dating because he is at least not required to pick up signals he is profoundly unable to read.

Eldridge's writing is deft and detailed, but Danny is the more fully developed and imagined character; unmanned by his past mistakes, sunk into gloom by his separation from his child, thinking a discussion of his mum's liking for kiwi fruit on her porridge is an effective chat-up line. Laura is more generic, longing for a child of her own and an escape from a rat race that has brought her financial rewards but no emotional fulfilment. She is perhaps loaded with too many clichéd worries and dreams, but she has a powerful voice.

Director Polly Findlay and movement director Naomi Said have orchestrated the couple's physical and psychological moves with uncanny precision and care. They are always putting space between each other, standing behind tables or awkwardly pushing around chairs; a clinch on a sofa is an agony of slithering, sliding discomfort. Danny doesn't have a clue where to put his arms. When he finally sits opposite Laura, as they eat fish finger sandwiches (another point of connection) it is a moment of physical resolution that reveals the coming to rest in his mind.

Beginning runs at the National Theatre until 14 November.