North Shropshire MP Helen Morgan was told by business secretary Grant Shapps that a scheme has been launched and they are "making sure it's expedited as much as possible".
In Shropshire, some 20,902 households rely on oil to heat their home and 4,554 households rely on tank or bottled gas. 1,982 homes have no central heating. In some areas, like Trefonen and Pant, more than half of households rely on oil to heat their homes.
They are due to get a £400 discount on their fuel bills but like payments for heating oil and LPG this is still yet to be rolled out.
Speaking after Tuesday's question in the House of Commons Ms Morgan said: “We’re midway through January, temperatures are below freezing and the Government still hasn’t sorted out payments to families in off-grid homes. It’s not good enough and ministers must work harder.
“Rural areas are always the last to get the help they deserve under the Conservatives.
“Once the scheme is belatedly rolled out, it’s really important the Government makes sure that everybody who is eligible is able to access the money as soon as possible regardless of their age or broadband speeds.”
Ms Morgan asked Mr Shapps if he "would consider a better public information campaign for those households and also support with access to applying for the scheme for those that struggle to get online.”
Mr Shapps said: “A lot of members will have park homes in their constituency, including my own, and the issue there has been more complex to get the money to them.
"She'll be pleased to hear that the pilot schemes actually launched yesterday to get that money out to them. It will be a process through the local authority and we're making sure it's expedited as much as possible.”