Volunteers handed out food parcels to hard-hit families on Monday and challenged the MP to come to Horncastle to see how serious the situation is.
They say families are struggling during the Covid-19 pandemic and fear some children could have gone hungry without the parcels.
Isobel Forrester, a leading volunteer at the larder, said she was ‘disgusted and disappointed’ with the no vote.
More than 100 people have taken to social media to criticise Ms Atkins and the Government although some posts have supported the ‘No’ decision.
Ms Atkins has hit back at the criticism and defended both her and the government’s decision.
As part of football star Marcus Rashford’s high-profile campaign, MPs last week had the chance to extend free school meals during the holidays.
However, Ms Atkins joined other Lincolnshire MPs in voting no.
Isabel Forrester, a leading volunteer at the Horncastle Larder, said she was ‘disgusted and disappointed’ with the Government and Ms Atkins.
MsAtkins said: “Throughout this difficult period, I have worked hard to support children, families and vulnerable people as your MP and as Minister for Safeguarding and will continue to do so.
“I reiterate the underlying truth that we all want to end child poverty. Let’s work together to achieve that.”
Mrs Forrester said she failed to understand why the Government had refused to extend free meals – despite overwhelming support for Marcus Rashford’s campaign .
She said: “People look at somewhere like Horncastle and probably don’t realise how many young families are struggling at the moment .
“The Covid-19 pandemic has definitely made things worse.
“Families are struggling. Parents have lost their jobs and incomes have been slashed.
“Covid has had a devastating impact on many lives.
“If she (Ms Atkins) can get to London to vote, she can come here and help us and see how serious the situation is.”
The larder - which relies on donations - has been handing out record numbers of food parcels during the pandemic.
Mrs Forrester thanked everyone who had donated.
She said support was needed ‘more than ever’ in the build up to Christmas – and with Covid restrictions likely to be increased.
She said St Mary’s Church donated proceeds from its recent Harvest Festival – as did the Edward Richardson School in Tetford.
Volunteers packed the parcels on Monday morning and families were able to pick them up from noon onwards.
The scheme has also been rolled out in Woodhall Spa and Coningsby .
Anyone who has not yet collected a parcel should ring 0759023501.
There was strong criticism of Ms Atkins’ no vote on social media.
Posting on the Horncastle News Facebook page, Rosemary Mocke said: “What’s the point of providing decent food once a day in term time and ignoring almost three months of holiday?
“On the whole, politicians of every political leaning, world wide, are so far removed from the reality of poverty, they haven’t a clue.”
Susan Steadman added: “This is disgusting. It’s ok for them (MPs) to have their posh meals and drinks. What about the real people that keep the country going?”
However, there was limited support for Ms Atkins.
One post on the Horncastle Community Facebook page said: “I’m sorry to read all this hatred and disgusting comments.
“I applaud the government for taking this stance. They have managed to find billions of pounds in help for this country and to slate a person like some of these comments are doing is shameful.
“There is not a bottomless pit of money. I am of the older generation brought up four children of my own and never ever let my children go hungry.”
In her statement, Ms Atkins said: “The Government has been working throughout the pandemic to get help and support to those who need it most, from the furlough scheme and grants for small businesses to increasing Universal Credit payments.
“Clearly, no one wants to see children go hungry.
“We may have different ideas on how best to ensure this does not happen but this underlying truth should not be lost in the debate.
“Last week, Labour held a debate about extending the free school meal programme via food vouchers in holiday time.
“Let me correct some inaccuracies that have been pushed on social media.
“This was not a vote to take free school meals away from children, nor was it a vote to stop Government action to tackle child hunger.
“In fact, it was a non-binding debate which happens most weeks on topics of the opposition’s choosing.
“Nothing changes at the end of such debates, regardless of how the House of Commons votes.
”This means that free school meals will continue as before and the Government will continue to fight child hunger.
“We just have different ideas from Labour on how to build sustainable programmes to tackle child hunger during the school holidays.”
Ms Atkins went on to highlight the number of schemes – including furlough – the Government had introduced to help vulnerable people.
She added: “We paid more than £820,000 to Lincolnshire County Council to provide food and other essential items to local people who need it most.
“I would like to thank all of the local businesses, community groups and people who have volunteered to help feed children in this time.
“This is a continuation of the public spirit and generosity that we saw during lockdown.
“I share your determination to end child poverty.
“Throughout this difficult period, I have worked hard to support children, families and vulnerable people as your MP and as Minister for Safeguarding and will continue to do so.
“I reiterate the underlying truth that we all want to end child poverty.
“Let’s work together to achieve that.”