Both Lincolnshire Police and Boston Borough Council have both put out calls on social media.
Boston Borough Council said: “Our business rates department is currently working hard in preparation of getting the government funding to businesses. Everyone will be notified in due course.
“Please refrain from calling our offices if you can, we are working as fast as we can.”
Meanwhile Lincolnshire Police said it had experienced an “extremely high volume” of calls following the Prime Minister’s lockdown broadcast.
“Please don’t call 999/101 unless it’s an emergency or you need a police response,” they said.
A number of councils have closed their face-to-face service centres in the face of the coronavirus outbreak, social distancing measures and staff shortages.
West Lindsey and North Kesteven both said they had seen an increase but were able to deal with the volume. However, advice included to use online measures to contact the authority if possible.
North East Lincolnshire said it had handled double the normal number of calls yesterday, taking 1,067 calls compared to the average of 500.
They have redeployed staff in response but urged people to follow advice.
Councillor Stan Shreeve, Cabinet member for Finance and Resources said: “Following Government advice in recent days, we have closed the customer access point in Grimsby and have redeployed staff from that service to respond to phone calls from the public.
“This is a time of tremendous change and this can cause some concern, but our staff are doing a great job in helping provide local information to our residents. Our message is for people not to worry and to follow the Government advice so we can beat this virus.”