The first Hugo Awards were awarded in 1953 at the 11th World Science Fiction Convention at Philadelphia. The first British-born winner was in 1955, since when there have been seventeen* more fiction awards to British-born writers.
Best Short Story
1955 - Best Short Story - 'Allamagoosa' by Eric Frank Russell
1956 - Best Short Story - 'The Star' by Arthur C. Clarke
1962 - Best Collection - Hothouse by Brian W. Aldiss
1969 - Best Novel - Stand on Zanzibar by John Brunner
1974 - Best Novel - Rendezvous With Rama by Arthur C. Clarke
1980 - Best Novel - The Fountains of Paradise by Arthur C. Clarke
1994 - Best Novelette - 'Georgia On My Mind' by Charles Sheffield**
2001 - Best Novel - Harry Potter and the Goblet of Fire by J.K. Rowling
2001 - Best Short Story - 'Different Kinds of Darkness' by David Langford
Best Novel
2002 - Best Novel - American Gods by Neil Gaiman
2003 - Best Novella - 'Coraline' by Neil Gaiman
2004 - Best Short Story - 'A Study In Emerald' by Neil Gaiman
2005 - Best Novel - Jonathan Strange & Mr. Norrell by Susannah Clarke
2005 - Best Novella - 'The Concrete Jungle' by Charles Stross
2007 - Best Novelette - 'The Djinn's Wife' by Ian McDonald
2009 - Best Novel - The Graveyard Book by Neil Gaiman
2010 - Best Novel - The City & The City by China Mieville
2010 - Best Novella - 'Palimpsest' by Charles Stross
British Science Fiction & Fantasy
Neil Gaiman has most wins with four awards. The most successful category is Best Novel. As well as eight full length works, Aldiss' award for Best Collection is a ninth book, while Coraline and Stross' The Concrete Jungle won Hugos, as part of or a full-length novel. The grand total of book wins is eleven.
Of the six awards for Best Short Story and Novelette, one was for a story in an original anthology, one for a story in the long-defunct Infinity, one each in Asimovs and The Magazine of Fantasy & Science Fiction, while two went to stories in Astounding, which later became Analog Science Fact / Fiction in 1960.
Only one winner came from a British magazine; an extract from Stand On Zanzibar appeared in New Worlds for November 1967.
Of the eight novel winners, the first three were SF, while the last five have been fantasy/ slipstream.
Notes
The reader will notice a distinct surge in winners since 2001.
* It was decided after much reflection to ignore the two Retro Hugos awarded fifty years after publication. While the Hugo Awards are retrospective, they are as contemporaneous as can be; by contrast, the Retro Hugos are nostalgia-driven.
** Charles Sheffield was born in the United Kingdom, and later emigrated to the USA.