British Weather
"Too Hot, Too Cold, Too Wet and Too Windy"—Dr. Xargle's Book of Earthlings
"In the Bible, God made it rain for forty days and forty nights; and that was still the best summer we had!"—Rhod Gilbert, Welsh Comedian
It's a bit of a cliché, but it's true. The longer any given conversation in Britain, the higher the chance that the weather will be mentioned at some point.
This is because it's so varied. It is not uncommon to have all four seasons in a single day.
John Cleese once told David Letterman, "We have a national holiday. It's called summer."
A big factor in this is prevailing winds. We have the Gulf Stream/North Atlantic Drift from the south west, which prevents the country from getting Canada-level cold (same latitude), but also brings storms. There's also cold winds from the north.
But the main reason is that the British are chronically shy and use the weather as a conversational totem, allowing conversation and agreement between strangers, without having to potentially invade their personal space (as described by Kate Fox in her book Watching the English). The most fundamental rule of 'weatherspeak' is to agree with the first speaker, even if you then immediately qualify it in such a way as indicates the opposite, eg, 'It's too hot today', 'yeah, it is, but I don't mind it myself'. Also it is often the only "safe" topic for any given two strangers to talk about and not risk some sort of argument. In the UK everything is Serious Business to someone. It's been said that the British have only two hobbies, complaining about the weather, and arguing.
Britain tends to have three seasons - a cold season, a wet season, and a cold and wet season. If you're lucky, there may be a week or so of sunshine between the latter two. Bill Bryson noted seeing a forecast of 'Warm and dry, with cooler and rainy spells' and commentated that it could be printed every day, and in fact might be for all he knew, and hardly ever be wrong, and that unless you decide to go hiking up Ben Nevis in your dressing gown, you can probably get away with wearing the same thing all year round. Provided it comes with a hood.
In seriousness, Britain is a temperate country. Breaking the 30 degrees Celsius level occurs once or twice year and 40 is unheard of (the UK record is 38.5 degrees in Kent in 2003). If it gets hot, expect at least one paper to have photographs of bikini-clad sunbathers—guaranteed, and very cold winters are also rare.
Heavy snow is rare (snow of any sort is rare in cities outside of Scotland, and it's pretty scarce there too) and occurs once or twice a year. Icy roads are a more common problem, with associated light snow. If it actually snows in any significant amount, expect traffic chaos and wall-to-wall news coverage. Whenever it snows in Doctor Who, there's generally an alien involved. However, over the past few years, Britain has seen an increase in the amount of snow fall, and the amount of time it has settled for. It has been so severe that in 2010 entire stretches of motorways were blocked for days, schools were shut across the entire country and Britain encountered its coldest winter for 30 years. (Older folk will often remember much bigger snowfalls When I Was Your Age, but this may be due to the Nostalgia Filter - although even though it will vary depending on where you were, the winters of 1947 and 1963 (both notoriously and damagingly cold and snowy) and 1978-9, 1981-2 and 1991 were all memorably bad).
The most obvious thing anyone notices is the rain. Virtually every day, somewhere will have a downpour. If you look at the weather forecast for Wales on any given day, it predicts rain. The East Coast is supposed to be drier, but even there it's not exactly dry. Get two or three days of hot weather and a thunderstorm will generally finish it off. Wimbledon is a case in point, and rain (or bad light) is a frequent play-stopper in cricket. Football, on the other hand... only if the pitch is too frozen to play on, or actually flooded, is a match called off. Rugby won't be called off for anything less than a direct meteor strike—and then, only for long enough to prop the posts back up.
It floods on occasions, especially in the Midlands. London is protected by the Thames Barrier (that thing with three sails near London City airport), although that's more against very high tides.
Wind can get pretty high, but the sea is too cold for hurricanes. We've had some close ones though. The Great Storm of 1987 is infamous, partly because of a weather forecaster named Michael Fish, who explained that there wasn't a hurricane on the way. He was technically correct - hurricanes occur by definition in the tropics - but there were definitely some hurricane-force winds. In the event of a storm, expect at least one picture of some brave/stupid (opinions may vary) souls braving crashing waves on a seashore. A favourite pastime of schoolchildren on a windy day is to lift their jacket up over their heads and walk into the wind. Way more fun than it sounds.
The UK also has a surprisingly high amount of tornadoes, having the highest number of reported tornadoes compared to land mass of any country (and this includes Scotland and Northern England where they are very rare). These are rarely anything like as strong as those in the US's Tornado Alley, and are less common.
Pack an umbrella and a rain coat, that's all we can say. In the words of the Prophet Connolly, "There is no bad weather, only bad clothing".
London, of course, will always have fog at some point of the story. In addition to natural fog, the burning of coal creates a lot of problems. In 1952 it is estimated that over 12,000 people died from four days of bad smog. Actual London, and indeed Britain in general, are today far less burdened with fog than some fictional works would have you believe, but their depictions can be given a bit more credence if set after industrialisation but before the passing of the clean air acts. Narrow river valleys Oop North are prone to mist and fog in winter, but it's rarely a London phenomenon nowadays.
Irish weather is like British weather, but worse (although not as cold as Scotland). Indeed, the main reason that the lovely English cricket 'n' strawberries summer exists is that Ireland absorbs all the rain that comes in from the Atlantic.
It's worth noting that British (and Irish) weather is actually far more temperate than it 'should' be, due to the Gulf Stream, and this is sometimes pointed out by commentators. Without the Gulf Stream, the British Isles would have a similar climate to Winnipeg, which is at the same latitude as the Isle of Wight. On the other hand however, Canada is colder than it should be as well, due to no natural barriers to the cold arctic winds straight from the North Pole. The warming effect of the Gulf Stream allows tropical plants to flourish in Wales and on occasion be grown as far north as Scotland.
One aspect of British and Irish weather that's often overlooked by writers used to lower latitudes is that the days are very long in the summer and very short in the winter. This is especially the case in northern Scotland, but is true of the UK and Ireland in general. There's no "midnight sun" like in the polar regions, but 10 pm sun can be expected in midsummer. This has led to some degree of Fantastic Religious Weirdness here on Earth: Britain's substantial Muslim community, and particularly those living in Scotland, have received numerous fatwas saying "No, you don't have to fast from literal sunrise to sunset, seeing as that's a 15 or even 20-hour fast for 30 days when Ramadan falls in the summertime. 6 in the morning to 6 at night is just fine."