The warning is in force from 12 noon until midnight on Sunday 18 June.
The likelihood of disruption has increased in some areas.
The warning start time has been delayed until midday.
The Met Office said:
‘A few outbreaks of thundery rain are possible overnight and during the morning, but the main likelihood of heavy showers and thunderstorms is during the afternoon and evening, with longer spells of thundery rain in places.
‘Some places may miss most (or all) of the rain, but others could see 30 mm in an hour or less, and perhaps a few spots seeing 60 to 80 mm within 3 to 6 hours.
‘There is also the potential for frequent lightning, strong winds and hail.
‘While uncertainties remain regarding the extent and focus, it is perhaps areas from London northwards across the Midlands, eastern England, east Wales and southern areas of northern England, that currently seem most likely to see disruption.’