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The criminals used the digger to steal the ATM machines, before loading them onto the back of a truck and speeding away, accompanied by two other cars.
During their escape, the thieves also deliberately collided with two police cars, causing damage, but no injuries.
The shop, in Whitfield, Kent, is thought to have been targeted in the early hours of Monday morning, and pictures circulated on social media show the large orange digger discarded outside the front of the premises.
The area surrounding the crime scene has since been closed off with police tape.
The supermarket did initially open up for business this morning, but then temporarily closed and reopened this afternoon.
An eyewitness confirmed that the three cash machines that are situated at the front of the store have been completely wrecked.
The bystander added that 'the digger bucket had damaged the overhanging roof too'.
@piersmorgan look at these disgusting scenes someone turning up at TESCO in Dover over the last few days whilst this virus is geiping this country! #worldsgonenuts pic.twitter.com/wGFCtceu09
- Samuel Lilley (@RailwaysToday15) March 23, 2020
Residents have been sharing their outrage on social media after the crime, which takes place against the backdrop of the ongoing Covid-19 outbreak in the country, and the supermarket chaos that has ensued alongside that.
One person wrote: "Disgusting scenes at a Tesco in Dover, someone turned up with a digger over the last few days a mist [sic] the crisis gripping this country!"
Another person wrote: "Only in Dover would someone steal the ATM machine up Tesco's... Seriously is this what it is going to come to???"
A statement from Kent Police appealed for witnesses to come forward.
It reads: "Kent Police is appealing for witnesses after cash machines were stolen from a supermarket in Dover.
"A digger is reported to have been used to remove two ATMs from a wall at Tesco in Honeywood Parkway, Whitfield at around 12.30am on Monday 23 March 2020.
"The machines were loaded onto a flat-bed truck, which was driven in convoy with two Mitsubishi Shogun vehicles.
"Two police vehicles which attempted to stop the group were rammed and damaged in Old Park Hill, Dover. No serious injuries were reported.
"Significant damage has been caused and detectives from the Kent and Essex Serious Crime Directorate are carrying out enquiries to locate those responsible.
"Anyone who witnessed the incident or has CCTV or dashcam footage that may assist the investigation is urged to call the appeal line on 01622 604100, quoting reference 46/52654/20.
"You can also call the independent charity Crimestoppers anonymously on 0800 555111 or complete an online form at www.crimestoppers-uk.org"
A Tesco spokesperson told LADbible: "Our Dover Extra is open and serving customers as normal following the incident last night and we're helping police with their enquiries."
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