Did this in fact happen? They seemed to still be a power up until the middle of it. Wouldn't that influence have continued in some form when Empire went to Commonwealth?
Probably the biggest reason for Britain's decline in power was industrialization in other nations, especially the US and Germany. Whereas early in the 19th century Britain had been the lone industrial power, beginning in the mid-19th century other players entered the field. In fact, US GDP per capita surpassing the UK's around the turn of the century. Thus, while the Britain's navy, empire, and large economy made it still a major power in 1914, it was not a super power in the same way one might view the US in the post-Cold War years.
At the end of the day, Britain's relatively small size and population made it unable to stay dominant over larger nations as they became industrialized, and the need for reconstruction after World War Two further re-allocated resources which previously might have been used to project global power. That being said, Britain was and remains a remarkably powerful and influential nation given its size.
The other responses posted here seem to have covered this well, but I can offer some insight in a different region which may have affected their apparent role as a "great power.":
So in the 1950s Nasser is going to come to power in Egypt (1952 coup starts it off). He is going to get rid of King Farouk, the British puppet, who was largely resented by the Egyptian people. Nasser, as to pay for the Aswan High Dam in 1956 would nationalize the Suez canal. The British in conjunction with France and Israel will stage a "tri-partite invasion" in Egypt as to force Nasser to de-nationalize the canal. The British did not want to lose what convenience they had via a Suez canal under their control. After all, it was their way to get to India. However, the US will intervene and force the retreat of the British, French, and Israelis. Pan-arabism will sweep the middle east and anti-British sentiments will follow. This was largely because of the imperialist tendencies of Britain exemplified in the Suez crisis, and lead to a deterioration of British influence, or power, in the entirety of the region.
Furthermore, Britain can also be seen attempting to infiltrate the middle east throughout the 50s. The Baghdad pact between Turkey and Iraq against Soviet aggression (1955) will be hijacked by the British and Nasser will heavily criticize Anthony Eden for the move on radio talks ("Voice of the Arabs"). So by the end of the 50s, the British lose their legitimacy in the middle east, and thus fall from prominence as a power, at least to some extent. Of course there was a plethora of other reasons which lead to this fall, but this was one way in which Britain would be diminished.