Foreigners, especially Americans, have some pretty strange misconceptions about how 'bad' British weather is.
In fact, as the ancient authors often used to state in early accounts of the British mainland, it is easier to argue that Britain has just about the best weather in the world.
Nonetheless, those who say the British weather is terrible are presumably responding to something.
1. I will define Britain for these purposes as the area bounded by London, Bristol, Glasgow and Edinburgh - since this contains a very high proportion of the population, and visitors seldom venture much beyond it.
2. Within this quadrilateral-ish zone, the weather is strikingly variable - notably there is a lot more rain in the west - about twice as much, such that a 'normal' day in Glasgow is rainy. Having lived there more than three years, I know from experience that this much rain does limit what you can do and how things look, especially as a tourist. But that is the extreme, the bulk of Britain to the South and East of Glasgow does not get anything like so much rain.
3. The British climate is more temperate, less extreme than just about anywhere.
Masses of people (I mean dozens, hundreds - never thousands) are only very rarely killed by the weather - by floods, storms, avalanches (!), heat etc - in the way that they are in North America and Europe - and even one single individual killed by the weather is rare and makes national news.
4. What is bad about the British weather is unpredictability, on a day by day - even hour by hour- basis. It is seldom you can be sure it will not rain on a given day; on the other hand it is seldom that the weather stays bad for long and there is always hope of imminent improvement.
(We do get - every few years - dry sunny midsummer and/ or icy-cold midwinter periods lasting multiple weeks - when there is settled High Pressure over the islands, and the weather stays the same day after day. People naturally remember these extreme stable periods, but they are uncharacteristic.)
5. My theory about 'bad' British weather is that people are responding to high latitudes - Britain is at a very high latitude compared with most populous countries; this means that day lengths are extreme (long days in summer, short days in winter), causing a considerable stress of the hormonal and neurotransmitter systems.
Those foreigners who spend the winter here are likely to experience seasonal affective disorder (SAD) of some degree of severity - lethargy,somnolence, irritability, asociability, carbohydrate craving and weight gain...
My hunch is that the bad reputation of British weather comes from extreme latitude rather than the actual weather.
Unless, that is, the disaffected foreigners who spread the bad 'rep' we have for weather had lived in the British rain-capitals of Glasgow or Manchester - in which case their bleak impressions were probably justified by experience.
(Note: The good news is that SAD is completely treatable nowadays, by the use of artificial bright early morning light. Which I suppose makes Britain paradise - as I look out at the cold rain lashing the windows... But yesterday was sunny and last week was warm - so I console myself that the weather will soon change. )