People trapped by flood water in a shopping mall near Sheffield have been told they can leave but were warned there will be severe delays due to “extreme weather conditions”.

Shoppers at Meadowhall had earlier been told to stay put by police and not to attempt to leave the mall after flooding left roads gridlocked.

Later on Thursday night, Meadowhall said: “The weather is ever-changing but the latest advice is to leave the centre as the traffic has eased but drivers may still encounter severe delays.”

It said: “For anyone who prefers to stay with us in the centre they are very welcome to do so. We encourage everyone to stay safe in these extreme weather conditions.” The centre said most people had left the mall by the time it officially closed at 10pm “but there are a small number of people who have chosen to stay with us for the time being. We will continue to look after them until they can return home safely.” It said the floods had not breached the building.

However, dozens of people were unable to leave and were forced to spend the night in the spent the night in the centre’s dining area.

The shopping centre had been due to hold its Christmas Live event at which its festive lights were to be switched on.

Thousands had headed to the centre, just off the M1, for the event, which was due to feature acts including Ella Henderson, Tom Zanetti and Jonas Blue. It was cancelled with just an hour’s notice as conditions worsened.

The centre has flooded before, in 2007, when the River Don burst its banks, inundating large parts of Sheffield. Hannah Crossley, 24, who was stuck inside Meadowhall, said that the river looked to be just centimetres away from bursting over the banks of the river.

“It’s not safe for us to leave,” she said before police lifted restrictions. “There are some children who went to the lights switch-on who are in pyjamas and can’t get home,” she said.

Some businesses close to the river closed early on Thursday when the water levels began to rise to prevent staff being trapped in buildings overnight.

Ethan Rylett, a 23-year-old sales representative at a dentistry supply business near Meadowhall, said he began to notice the rising water level from his office around noon, and was dismissed from work in the early afternoon.

“I’m stressed about the impact it could have on the business,” he said. “We did as much as we can to get as much stock from ground level but we’ve got a lot of technical equipment that’s built in to the workstations,” he added.

Students in university accommodation on the banks of the river were forced to abandon their cars, as vehicles were submerged by flooding in the underground car park. “A lot of people who own cars here are very stressed,” Lucy Pearson, a 20-year-old student said. “It looks like there are cars that are being consumed by the water and are now in too deep to be retrieved.”

On Thursday evening train services were affected by flooding across the Pennines and South Yorkshire, and tram services between Rotherham and Sheffield were hit by the bad weather.

The Met Office issued an amber warning for heavy rain until 6am on Friday for an area between Sheffield, Manchester and Bradford. It has also issued yellow warnings for surrounding regions stating that 40mm (1.5in) of rain had fallen in the Sheffield area between midnight and noon on Thursday, half of the average November rainfall in the area.

Sheffield city council said seven roads in the city were closed because of flooding and the Millhouses public park had been closed owing to concerns about the rising level of the River Sheaf.

Residents have been evacuated from 35 homes in Mansfield following a mudslide caused by heavy rain, Nottinghamshire police said. The force was called to Bank End Close alongside the fire service and Mansfield district council just before 5pm following concerns for the safety of people living in the houses. Drivers are being told to avoid the area.

Chris Wilding, flood duty manager at the Environment Agency, advised people to stay away from swollen rivers and not to drive through floodwater. He added: “Just 30cm of flowing water is enough to move your car. Our incident rooms are open and we are working closely with local authorities and partners to reduce the risk of flooding. Our field teams are ready to deploy temporary flood barriers to help protect people and property if needed.”

Rail firm Northern issued “do not travel” advice for passengers using three routes. They said flooding had closed the lines between Sheffield and Gainsborough, Sheffield and Lincoln and Hebden Bridge and Manchester Victoria. The firm said that roads were also closed in the corresponding areas, meaning “customers should not attempt to travel”.

Meanwhile, South Yorkshire police issued alerts including one that said: “Please adjust your driving to suit the extreme conditions during the next 24 hours. We have more rain forecast and many roads have standing water which varies in depth, so please drive with caution and reduce speed to allow time to react.”