British people may get more money in their pockets, but everything is way more expensive than other countries, so you have to think again if you think UK people are rich
also, USA's economic boost, drifted UK, since these countries have many links, and common language, so UK for many is considered a USA link in Europe
Many reasons behind this, here's a few possible ones:
1) Stable governance - very important in making a country rich. Britain hasn't had a revolution in 400 years meaning that people from around the world could trust that investment in Britain was secure and that money from Britain's banks was stable. It also gave people confidence within the UK to innovate, create industry and jobs.
2) Industrialisation - The Industrial Revolution occurred first in Britain so it was the first country in the world to industrialise. This meant that the island became a centre for manufacturing and was at the forefront of mechanisation. It could sell its goods across the world and through its empire.
3) Empire - Britain was an outward looking country and took empire very seriously. It built up the biggest Navy in the world to protect its markets. It also had sources of cheap commodities (the colonies) to give its manufacturers at home a competitive advantage. In the early 20th century Tariff Reform was put forward by the Conservatives which proposed taxing goods from outside the Empire. This shows just how powerful Britain was and why it became so rich because of it.
4) Entrepreneurship - Britain became a centre for science, engineering and technology, drawing the best minds from all over the world into world class Universities (Oxford, Cambridge, London etc.) this in turn gave the country a competitive advantage and produced wealth.
Hope these reasons help, these were the main reasons Britain became rich and most of them are still true today with the notable exception of Empire. Britain relies heavily on the Service industry and Finance now which gives it the sixth largest economy in the world - the country has good trading links with several European Union countries (11.5% of its exports to Germany, 8.9% to the Netherlands, 7.4% to France..etc) and to the United States (10.6% of exports)
Liberal democracy starting with the Magna Carta and evolving (violently and bloodily) into a constitutional law which is both adopted and emulated across the western world. This systematcally eliminated the ability of the ruling elite to squander the wealth of the country. Instead, re-distribute it in the form of education, social welfare and infrastructure whilst retaining the best in entrepreneurial free-trade practices. Fraternité, egalité, equalité to borrow form the French.
A culture of stoicism in the face of adversity and a fierce determination that 'stays calm and carries on'. The ability to rapidly adapt to and indeed embrace change - retaining the best and eschewing the failed. (Indeed, I suggest it is the very inability to rapidly adapt which will utimately be the Achilles-heel for the emerging eastern economies of China and India.)
A state and culture which promotes freedom of expression, the freedom of individual choice and the celebration of innovation.
A state in which the framework of democratic law, trade and innovation continues evolving and is unencumbered by religious dogma.