LONDON, Jan 5 (Reuters) - Major rivers across Britain were flooded on Friday after heavy rain, with the government issuing more than 300 flood warnings, travel operators announcing serious disruption and around 1,000 homes suffering damage so far.

A succession of storms in recent weeks meant prolonged rainfall that started on Thursday fell on saturated ground and quickly caused already-swollen rivers and waterways to burst their banks across England and Wales.

The storms have also caused flooding in other parts of Europe in recent days. The River Trent in central England flooded, prompting the local authority to declare a major incident. London's fire service said it had to escort around 50 people to safety late on Thursday after a canal in the east of the capital overflowed.

"We have woken up to, as many people will see, to a very wet situation across the country," Caroline Douglass, the director in charge of flood management at the Environment Agency, told the BBC.

Douglass said around 1,000 homes had so far been flooded. Great Western Railways said its lines in three parts of the south of the country were closed. Roads in the worst affected areas were also closed.

More rain was forecast for Friday, albeit not at the same intensity as seen overnight, with drier weather expected to follow.