Workers and shoppers were moved from the site at 11am after deep water started to flood through one of the entrances.
Priory Meadow in Hastings, East Sussex, was cordoned off as firefighters attempted to pump water out of the precinct.
Nearby streets in the town centre had also flooded and East Sussex Fire and Rescue Service warned people to avoid the area.
The brigade said there were no plans to evacuate any of the surrounding properties — but emphasised this is subject to change as it continues to monitor the weather.
A spokesman added: “Public safety is a key priority and we would ask members of the public to only contact us in relation to flooding where there is a risk to life.”
The wet weather hit parts of the South and West of England yesterday, as well as Wales.
The Environment Agency currently has 42 flood warnings and 112 flood alerts in place across the UK, with more of the country set to be hit as the rain and wind moves North.
Met Office chief meteorologist Andy Page said: “The wet and often windy theme is continuing through the weekend for many, with plenty of showers and some longer spells of rain possible in some areas, which has the potential to cause disruption.”
Yellow weather warnings are in place in London and the South East today, as well as in parts of Northern Ireland and the East of Scotland.
The warning in Scotland, where areas were flooded by Storm Babet earlier this month, runs until tomorrow.
The Met Office said flooding remains a high risk there due to the already “saturated” ground.