The new express supermarket at the former Parsons garage in Oxford Road opened in April following a long planning battle after the borough council originally refused planning permission. But the decision was quashed at a three-day appeal in 2012.

However, neighbours are accusing Tesco of breaching the conditions set out in the appeal that deliveries will only be made between 9am and 3pm and 6pm to 8pm on weekdays, to avoid peak periods, because they are worried the large articulated lorries pose a risk to youngsters making their way to Oxford Road Community School across the road.

Father-of-two Glenn Burden, from Prospect Street, said: “My concern is articulated lorries are pulling into and out of the store when parents are walking young children to school or pushing buggies.

“This really needs to be stopped and controlled by not letting lorries enter and exit the place when people are going to school. The last thing anyone wants to see is a kid being hit.”

His complaints are being echoed by Battle ward councillors Chris Maskell and Sarah Hacker, who said: “We fought hard against this planning application, and the council refused it because of concerns about road safety.

“Despite this the Government inspector saw fit to overturn this judgement. Sadly it appears we are being proved right. We will do anything in our power to ensure children are kept safe on their way to school.” But Tesco spokesman Jack Pearson said a management plan, which will include delivery times specifications, has been submitted to the borough council and until it is ratified there are no conditions on when deliveries can be made.

Mr Pearson stressed that neither the parents or the school have lodged a complaint with the company.

He said: “We take the safety of customers and pedestrians near our Oxford Road store extremely seriously and deliver outside of peak times, avoiding the local school run in the morning and afternoon.

“We of course will only deliver during the times agreed with the council and would be very happy to speak to any local councillors, to see if there is anything else we can do to help.”