There is real intimacy and emotional generosity to this psychological mystery from Joanna Hogg – a personal movie which appears to come from the same universe as her earlier Souvenir films – or one very much like it. It’s a ghost story whose purpose is something other than scaring you, a film about the enigma of your parents’ lives, their unknowable existences before you were born and indeed after you were born; that feeling that your parents are simultaneously as familiar as a pair of old slippers and yet also a Sphinx-riddle, withholding from you the meaning of your life and death. And perhaps the only way of cracking the code, solving the problem, is finally to become your mum or dad, to feel what they feel from the inside, and yet even then never to be sure.

Tilda Swinton gives a touching and wittily differentiated doppelgänger performance as a film-maker who brings her elderly mother to a country house hotel for her birthday – the hotel was once in fact a private estate where her mum spent time as a little girl. She hopes also to get some work done on her latest screenplay. Swinton of course plays both roles: both daughter and the rather amiably grand and patrician mother, whose authentic membership of the upper classes is signalled by the fact that she has brought her dog with her – Louis. (Although Hogg playfully confounds accepted class signifiers by having the mother expect fish knives at dinner – in defiance of Betjeman’s famously satirical dismissal of this kind of cutlery.)

Hogg contrives Swinton’s daughter and mother nearly always to have conversations in shot-reverse-shot exchanges: you find yourself wondering when they are ever going to appear on screen together at the same time – if only cheated in a long shot. When it happens, it is the signal for an existential shift. The hotel is highly disconcerting: there was some problem with their booking – and yet there appear to be no other guests. The daughter is kept awake at night by creepy and unexplained banging noises from the other (empty) rooms. The receptionist (Carly-Sophia Davies) behaves with sub-Fawlty truculence and is unsubtly rude while serving the two women’s dinner in the gloomy mausoleum-style restaurant. But there is a very nice concierge (Joseph Mydell) who divines the daughter’s unhappiness and who turns out to be playing the mournful flute music that we hear at the beginning, a kind of diegetic reveal which would be funny in another kind of film.

The mother is pleasant, good-natured, delighted at her gifts and being made a fuss of, and yet the daughter senses – as she has clearly sensed throughout her life – that her mother is suppressing some terrible sadness or pain. And she is devastated and even angered that her mother simply won’t tell her. In fact, coming back to this old house does bring back memories, many sad, and the mother is perplexed at her daughter’s tearful overreaction. The older woman, with all her generation’s reluctance to indulge their emotions, is appreciative (if a little embarrassed) about all the younger woman is doing. The daughter, for her part, is mortified by the knowledge that her mother is saddened by her childlessness; by the fact that she is to be eternally the daughter and never the mother. And it is genuinely unnerving when Swinton’s mother somehow looks older in each shot, gazing into the lens, stricken by the future. What is happening in this ghost-hotel? Sometimes it looks like a location for Rattigan’s Separate Tables – but also appears to contain the final scenes from Kubrick’s 2001.

There is such closeness and tenderness in this small-scale film: I loved the moment when the mother briefly trips or stumbles walking up to the restaurant table and the daughter is instantly alarmed at the possibility she might fall, and then in the next microsecond has to convert that palpable alarm into something humorous and reassuring. The Eternal Daughter is a serious, gentle moment of self-revelation for Hogg.

• The Eternal Daughter screened at the Venice film festival, and is released on 24 November in UK and Irish cinemas.