On Tuesday morning, Dorset Council said it had “begun the process of recovering the vehicle”.
A spokesperson said: “We appreciate the public’s patience and understanding.”
Beaminster councillor Craig Monks said: “The reality of being disconnected from a utility like the internet is havoc for residents and business in Beaminster.
“Accidents happen but we need to urgently restore connection.”
Silvana Bandini, owner of the Ollerod restaurant, said his landline was also down and he was using his mobile phone as a hotspot to access “basics” such as emails, booking systems and card payments.
He said: “Everything runs wirelessly – our printer is connected via wi-fi, so we can’t print anything.
“Our music system is Sonos, which is all connected via wi-fi, so we have no music.”
Beaminster Library said it was offering free wi-fi from 10:00 to 13:00 for anyone who needed it.
Dorset Police said officers were called to “a report of a vehicle fire following a single-vehicle collision in Beaminster”.
A spokesperson said: “The driver was not in the vehicle and enquiries [are being] carried out to try and locate them.”