Boris Johnson heads to the north of England later, after the Tories' biggest election win since 1987.
The Labour leader says he will not walk away from the role until a successor is chosen.
She says she is "proud" to have been the Liberal Democrats' first female leader, as she steps down.
Scotland's first minister says the SNP election victory strengthens the mandate for another referendum.
New rail timetables come in on Sunday, with more and speedier services promised on some routes.