The warning has been put in place from midnight on Sunday to 3pm on Sunday afternoon.
The forecaster warned that a short period of heavy rainfall may bring “some localised flooding and transport disruption”.
This means bus and train services will probably be affected and flooding will impact homes, businesses and journey times.
Other parts of the UK have a weather warning in place on Friday and Saturday – but the battering conditions are only due to hit London towards the end of the weekend.
Here’s what the Met Office said to expect:
Friday: Mild but breezy and rather cloudy for much of the day, with spells of rain and showers making progress eastwards. Perhaps becoming more generally dry, bright and less windy later on, although coastal districts may retain a few showers. Maximum temperature 16 °C.
Friday night: Mainly fine during the evening, with showers fading in coastal districts. A further swathe of rain is likely to reach western parts to end the night on a strengthening breeze. Minimum temperature 8 °C.
Saturday: Cloudy, breezy and wet during the morning, the rain perhaps turning heavy briefly before clearing eastwards into the afternoon. Drier and brighter later, with sunshine and perhaps the odd shower. Maximum temperature 15 °C.
Outlook for Sunday to Tuesday: Successive bouts of wet and windy weather making progress eastwards leading to temperatures below average. Some sunny spells are also likely, these perhaps most widespread on Monday.