As Meat Trademark's answer points out, the clear out of universe answer is that the show originated in England (although is now produced in Wales) and the majority of its domestic audience is English.
In universe, there isn't much to explain the Doctor's connection to England, but I can offer some clues.
He is certainly committed to defending the Earth
In The Christmas Invasion, the 10th Doctor beats the leader of the Sycorax in single combat as Earth's Champion. He then tells the Sycorax:
By the ancient rites of combat, I forbid you to scavenge here for the rest of time. And when go you back to the stars and tell others of this planet, when you tell them of it's riches, it's people, it's potential. When you talk of the Earth, then make sure that you tell them this. It is defended.
Revived series, 2005 Christmas Special: The Christmas Invasion (Transcript from chakoteya.net)
In The Eleventh Hour the 11th Doctor acknowledges (but downplays) his connection to Earth:
ATRAXI: You are not of this world.
DOCTOR: No, but I've put a lot of work into it.
Revived series, Season 5, Episode 1: The Eleventh Hour (Transcript from chakoteya.net)
He then goes on to show the Atraxi the many enemies who have tried to invade the earth and all the Doctors who have stopped them.
He admires the English
He does express admiration for the English from time to time. For example in The Empty Child the 9th Doctor says to Nancy:
Right now, not very far from here, the German war machine is rolling up the map of Europe. Country after country, falling like dominoes. Nothing can stop it. Nothing. Until one, tiny, damp little island says no. No. Not here. A mouse in front of a lion. You're amazing, the lot of you. Don't know what you do to Hitler, but you frighten the hell out of me. Off you go then do what you've got to do. Save the world.
Revived series, Season 1, Episode 9: The Empty Child (Transcript from chakoteya.net)
He gets attached to what is familiar
While the Doctor has shown his appreciation for Earth in general and the English in particular, there is no need to assume that they are especially deserving of this appreciation. We know that he becomes attached to his companions and can't bear to lose them.
I believe we should think of the people of Earth and of England as similar to companions. He probably didn't choose them, but by chance the TARDIS took him to England several times. He got used to the place and an affection developed.
UNIT has bases in England
In The Stolen Earth (episode 12 of season 4 of the revived series), we see that UNIT HQ is in New York, but UNIT clearly has significant bases in England as well. For example:
- The Third Doctor worked for UNIT in England.
- In The Day of the Doctor (50th Anniversary Special) we learn that the Black Archive is in London.
The Doctor often works closely with UNIT, so it makes sense for him to visit places with UNIT Facilities.
Footnote: Revived series episodes set on Earth but not in England
I reviewed all the stories of the revived series from season 1 through 11, and while the overwhelming majority of Earth-based episodes took place mainly in England (I counted 54), there were many primarily set elsewhere.
- 8 in the USA. Dalek. Daleks in Manhattan, The Impossible Astronaut, The Day of the Moon, A Town Called Mercy, The Angels Take Manhattan, The Return of Doctor Mysterio, Rosa.
- 4 in Scotland. Tooth and Claw, Under the Lake, Before the Flood, The Eaters of Light.
- 2 in Wales. The Unquiet Dead, Boom Town.
- 2 in Italy. The Fires of Pompeii, The Vampires of Venice.
- 2 in Scandinavia. The Girl Who Died, It Takes You Away.
- 1 in France. Vincent and the Doctor.
- 1 in Germany. Let's Kill Hitler.
- 1 in Central Asia. The Pyramid at the End of the World.
- 1 in South Asia. Demons of the Punjab.
- 1 at the North Pole: Last Christmas.