The temperature topped 34.6 C in Wisley, England, while Scotland and Northern Ireland saw their hottest days of the year.
The outgoing PM is offering "access talks" with the civil service to Labour leadership candidates.
The government says it is still planning to publish the spending proposals before a Nato Summit on 7 July.
A body is found in the search for Lilly, 14, who was reported missing on Saturday.
Six people have been taken to hospital after the crash on the A484 near Kidwelly.