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Thousands of schools remained closed in Britain today despite improving weather conditions after yesterday's heavy snow paralysed southeastern England.

Angry parents complained of confusion and contradictory messages. Head teachers first promised yesterday that classrooms would be open today, then changed their minds as weather forecasts appeared to point to more blizzards — only to realise this morning that conditions were not as bad as had been feared, and that classes could have gone ahead.

All of Surrey's 403 schools remained closed today, although main roads were passable and most trains were running. Birmingham and Bradford local authorities also ordered all their schools to close for a second day.

"We are giving children the message that when things get difficult you should just stay at home and have fun," said Margaret Morrissey, of the Parents Outloud campaign group.

"Then, when they keep taking sick days from work when they grow up we wonder why."

She called for an emergency plan to be introduced to allow more schools to stay open in the event of bad weather.

Tony Reeves, the chief executive of Bradford council, defended the decision to keep schools shut today because of the "very severe weather forecast".

He said: "This decision has not been taken lightly, but it is in the best interests of both children and parents to ensure their safety and to allow parents to make child care arrangements, including informing their employers where necessary. It is schools being closed at short notice which causes most disruption to residents and the economy."

In Essex, where more than 400 primary and secondary schools were closed again today, the local education authority was advising parents to listen to local radio stations for further updates on school closures and openings.

More than 100 schools in Kent remained closed, although to add to the confusion some that were shut yesterday were hoping to reopen at 10.30am today.

More than 40 schools were closed in Camden, North London, although again some were planning to reopen. Schools in Newham and Merton also remained shut. In Westminster, parents were advised to keep children at home to avoid weather conditions "likely to severely hamper safe travel for pupils and teachers". In Lambeth, South London, 23 schools were either closed or "almost certain to close".