The tourist view of Britain involves lots of formal ceremonies. Some people have drawn the conclusion from this that the British are rather formal in their general behaviour. This is not true. There is a difference between observing formalities and being formal in everyday life. Attitudes towards clothes are a good indication of this difference. It all depends on whether a person is playing a public role or a private role. When people are 'on duty', they have to obey some quite rigid rules. A male bank employee, for example, is expected to wear a suit with a tie, even if he cannot afford a very smart one. So are politicians. There was once a mild scandal during the 1980s because the Leader of the Opposition wore clothes on a public occasion which were consider too informal.
On the other hand, when people are not playing a public role - when they are being themselves - there seem to be no rules at all. The British are probably more tolerant of 'strange' clothing than people in most other countries. You may find, for example, the same bank employee, on his lunch break in hot weather, walking through the streets with his tie round his waist and his collar unbuttoned. He is no longer 'at work' and for his employers to criticize him for his appearance would be seen as a gross breach of privacy. Perhaps because of the clothing formalities that many people have to follow during the week, the British, unlike the people of many other countries, like to 'dress down' on Sundays. They can't wait to take off their respectable working clothes and slip into something really scruffy. Lots of men who wear suits during the week can then be seen in old sweaters and jeans, sometimes with hotels in them. And male politicians are keen to get themselves photographed not wearing a tie when 'officially' on holiday, to show that they are really ordinary people.
This difference between formalities and formality is the key to what people from other countries sometimes experience as a coldness among the British. The key is this: being friendly in Britain often involves showing that you are not bothering with the formalities. This means not addressing someone by his or her title (Mr, Mrs, Professor etc), not dressing smartly when entertaining guests, not shaking hands when meeting and not saying 'please' when making a request. When they avoid doing these things with you, the British are not being unfriendly or disrespectful, they are implying that you are in the category 'friend', and so all the rules can be ignored. To address someone by his or her title or to say 'please' is to observe formalities and therefore to put a distance between the people involved. The same is true of shaking hands. Although this sometimes has the reputation of being a very British thing to do, it is actually rather rare. Most people would do it only when being introduced to a stranger or when meeting an acquaintance (but not a friend) after a long time. Similarly, most British people do not feel welcomed if, on being invited to somebody's house, they find the hosts in smart clothes and a grand table set for them. They do not feel flattered by this, they feel intimidated. It makes them feel they can't relax.
It is probably true that the British, especially the English, are more reserved than the people of many other countries. They find it comparatively difficult to indicate friendship by open display of affection. For example, it is not the convention to kiss when meeting a friend. Instead, friendship is symbolized by behaving as casually as possible. If you are in a British person's house, and you are told to 'help yourself' to something, your host is not being rude or suggesting that you are of no importance - he or she is showing that you are completely accepted and just like 'one of the family'.
In the last decades of the twentieth century, the general amount of informality has been increasing. Buffet-type meals, at which people do not sit down at a table to eat, are a common form of hospitality. At the same time, the traditional reserve has also been breaking down. More groups in society now kiss when meeting each other (women and women, and men and women, but still never men and men!).