The answers are historical and economic as well.
Put simply, musician and singers tend to carefully emulate the singers who influence them.
Rock and roll, rhythm and blues, jazz, the blues and gospel were all styles of music that originated in the USA. The USA music industry, from the 1920s through the 1950s and ever after, recorded lots of this music onto lacquer and then vinyl records, mass-produced and effectively marketed some extremely popular hit records, making stars out of certain singers, and then exported the records to other nations outside the USA.
However, up until the late 1950s, British audiences preferred listening to music that was indigenous to the UK, and possibly from Europe. Very little vocally-oriented music from the USA was popular in the UK, and the styles of music were thoroughly different. American forms like rock and roll, rhythm and blues, jazz, the blues and gospel were not popular in the UK at this time. If you do some research and listen to records that were popular in the UK in the 1930s, 1940s, and 1950s, you will be very surprised to discover that the singers on these records sound thoroughly British. The singing style, particularly in the 1930s and 40s, is markedly almost classical and operatic compared to the way that modern rock and pop music sound. This British music didn't use guitars and didn't have the American back beat, either.
In England, starting around 1959, audiences turned their attention to music recordings imported from the USA, which became very popular. I cannot cite a source for this, but it seems to me that this was coincident with the UK's lifting of a longstanding high tariff on all kinds of imported goods. I believe that recorded music from the USA was imported at a much higher rate after this, and the music that was imported sold well.
At the same time, as I understand it, all radio broadcast in the UK was granted exclusively to the BBC (British Broadcasting Corporation) which was tightly centrally controlled. The BBC originally didn't play much if any music from the USA, certainly not rock and roll. However, around the early 1960s, illegal, unlicensed "pirate" radio stations began to operate in the UK. They played a lot of music from outside the UK that the BBC was not playing then -- particularly rock and roll. Surely this had something to do with the UK public becoming more aware of music from the USA.
For these reasons, then, in the United Kingdom, from the early 1960s and thereafter, there was a fad for American music, and the English bands were performing it and emulating it. Musical groups from the Rolling Stones and the Beatles onward started by playing cover tunes: by performing the same songs heard on hit records from the USA, but also by carefully emulating all aspects of the musical and singing styles of those recordings. Their audiences at the time had heard the original records from the USA, and the musicians wanted to sound as much like them as possible.
Once these English bands started writing their own original music, they tended to continue to pay tribute to their influences from the USA by singing in the same style they heard on those records from the USA. Audiences had become accustomed to it, demanded it, and paid money for it. Thus, even when these British bands began to write original music, their singers wrote lyrics and sang them in a carefully-emulated American style. Those that did tended to be more successful and sell more records than bands that continued to sing in the British style. This stylistic practice continues to this day.
Do not lose sight of this: ultimately, when you are talking about the USA singing style found in rock and roll, rhythm and blues, jazz, the blues and gospel you are talking about the style of African-American singers, with words and lyrics written in the colloquial style and dialog of their community, and singing styles that came from only two sources: rural black workers' blues ("Delta blues"), and African-American church worship music ("black gospel"). Everything from the rock era, even that sung by white musicians in the USA, is in emulation of the core styles of African-American singers and lyricists.
So the British singers you are asking about all, ultimately, emulated black singers from the USA, not white singers from the USA. This is because the white rock singers from the USA were themselves emulating the black singers from the start. Everyone concerned freely acknowledges this.
If you would like to see an entertaining and humorous portrayal of all of this in a fictional motion picture, check out the 1991 Irish movie "The Commitments", in which a group of young Irish musicians in present-day 1990s Ireland create a band to carefully emulate African-American rock and rhythm and blues from the 1960s.