Britain is likely to enter arduous talks on its exit from the European Union without a deal to keep Prime Minister Theresa May in power as negotiations with a Northern Irish "kingmaker" party grind into a second week.

After a tumultuous week that pitched Britain into its deepest political crisis since the Brexit referendum a year ago, May's future was uncertain, darkened by her botched gamble on a snap election and muted response to a deadly fire in London.

Fighting for her political survival, May has been trying to strike a deal with a small Northern Irish Protestant party to avoid a second election that could delay Brexit talks and damage the $2.5 trillion economy.