Harvey Shine (Dustin Hoffman) works as a jingle writer for television commercials in Manhattan, a job not in keeping with his one-time aspiration to be a jazz composer and pianist. We see him at work and he is very good at what he does. However, his boss does not seem impressed with his latest output. As Harvey departs for London to attend his daughter Susan's wedding, his boss actually suggests that he spend more time there than he had originally planned. Harvey declines, making the point that he needs to be back for an upcoming pitch to an old client. His boss insists that it is being done by other musicians, and that Harvey's latest work was his last chance to keep his job.
On the plane, Harvey tries to chat up a fellow passenger, but she is having none of it. He is left sitting there with egg on his face and we come to regard him as even more of a loser.
Meanwhile, we witness the mildly strained relationship between Kate Walker (Emma Thompson), a single Londoner, and her mother, whose husband left years earlier. Kate tries to reassure her mother that despite being single, she may yet find a man. Further, Kate tells her mom to quit worrying about the new Polish neighbor who has moved in next door and seems to be stacking a lot of firewood.
Upon arrival at Heathrow Airport in London, Harvey encounters Kate at her job collecting statistics from passengers as they pass through the terminals. She attempts to question him about his reasons for visiting the UK. Tired and anxious to get to his hotel, Harvey brusquely dismisses her when she approaches him to ask questions.
Harvey heads for the hotel to check in and discovers that he is the first one to arrive. Upon calling his daughter to double check where everyone else is when they were all supposed to be staying together, he learns that his ex-wife Jean actually rented a house to accommodate family and friends from the States and he is the only one at the hotel.
After a brief nap, he showers and hurriedly dresses. On the way to the rehearsal dinner in the taxi cab, he realizes the anti-shoplifting device is still attached to the sleeve of his jacket. And to make matter worse, he has worn a white suit (thinking this was requested) while all the other men wore black. During the meal, it becomes increasingly clear Harvey is considered a mere guest and the role of father of the bride has been delegated to Jean's husband Brian. To add insult to injury, Brian stands to give the toast, and recollects the vacation they all spent in Rome, and his stepson-in-law-to-be embraces him and calls him Dad. Just before leaving back to his hotel, when Harvey tells Susan (with whom he has shared a strained relationship since his divorce) that he will be attending the ceremony but not the subsequent reception because he needs to return to the States for an important meeting, she informs him she has asked Brian to give her away.
Meanwhile, Kate is set up on a blind date by a well meaning co-worker that does not go well. When she returns to the table after taking yet another call from her mother, she discovers her younger date has invited some of his younger friends to join them. Feeling unwanted and excluded from the conversation, she eventually excuses herself and goes home. As it turns out, Kate's increasingly neurotic mother seems convinced that her Polish neighbor is some kind of murderer because she sees him toting strange looking, lumpy packages into a shed in the back yard.
The following morning Harvey attends Susan's wedding, but heavy traffic delays his arrival back to Heathrow, and he misses his plane. When he calls his boss Marvin in NYC to inform him he will be returning a day later than planned and that he will try to get there as soon as possible, he is told that he is fired.
In his glum mood, Harvey makes his way to the airport bar and starts slugging down scotch, determined to drown his sorrows. Kate is sitting in the lounge reading a novel and drinking wine when she notices Harvey. She makes a barb to him about the drinking being a big help to whatever is bothering him and he fires back about her reading a trashy novel and drinking chardonnay not being so much better.
They gradually warm to each other over the course of their salads. After an awkward goodbye at the exit, where Harvey wistfully watches Kate walk away, he decides to follow her to the Heathrow Express and upon arrival at Paddington station, asks if he can walk her to her writing class on the South Bank. She accepts his offer and is pleased when he offers to meet her after class.
As they stroll along the River Thames, Harvey mentions he is missing Susan's wedding reception, and Kate urges him to go. He finally relents, but only if she will accompany him. When Kate insists she is not properly dressed for such an occasion, Harvey buys her a dress and the two head to the Grosvenor House Hotel, where they are welcomed warmly by Susan and her new husband Scott. When the father of the bride is called upon to make a toast, Brian rises and begins to speak until Harvey taps his glass and reminds him who the real father of the bride is. He then delivers an eloquent speech that redeems him with his daughter and endears him to Kate.
Following the reception, Harvey and Kate walk and talk until dawn. They exchange a single, gentle kiss and agree to meet again at noon at the same place, a cafe near a water park. They are both excited about the upcoming rendezvous, but after running up the hotel stairs too quickly, Harvey suffers an attack of arrhythmia! Paramedics rush him to the hospital, where he protests to doctors that he is fine and must leave to meet someone. The doctors insist that he must stay for further tests.
Kate buys some flowers and does her makeup in anticipation of seeing Harvey again. She waits at the cafe where they agreed to meet, yet he is still in the hospital, unbeknownst to Kate. After a long time waiting, she leaves alone, crushed and rueful.
Harvey immediately attempts to contact Kate after he is released from the hospital, but is surprised to receive a call from his ex-boss Marvin, who explains how his superiors like Harvey's latest work so much that he wants him to return to his job right away. Harvey pauses and then tells Marvin that he no longer wants the job.
Kate visits her mother again and discovers that the Polish neighbor has left a rather large smoked ham. Turns out that he is not a killer after all, just a meat smoker. Kate then returns to her job taking surveys at the airport, and when Harry calls her there, she refuses to take his call.
Harvey rushes to the airport to redeem himself with Kate but she has left for the day. Her workmates are suspicious of him at first but know that she likes him, and let him know that she is at her writing class. He tracks her down after class and reveals why he missed their rendezvous. Overly cautious about romance because of so many past disappointments, Kate initially resists his suggestion that they see what the future might bring them, but finally agrees to give things a chance. When she asks Harvey how it will work, he replies that he does not know, "But it will, I promise you that."
As they walk away, Kate takes off her shoes to make her closer in height to the shorter Harry. He says, "I think you're my kind of girl." When he recalls that she never did ask him the questions from her airport survey, she asks for his name and residence, to which he replies, "I'm in transition."
Over the end credits, we see that Kate's mom has gone to visit her Polish neighbor to thank him for the ham. The neighbor invites her to come into his house, and after some feigned hesitation, she agrees to enter.