CAP held talks with the big six energy firms at Westminster last night to raise the issue of prepayment meters.
The meters work through up-front payments, similar to pay as you go mobile phone deals.
These prepayment meters are often more expensive than direct debits but are rife in deprived areas, despite being the more expensive way of heating a home.
CAP Chief Executive, Matt Barlow, said: "We have been at Westminster to demand justice; to say that those who have the least in society should at least be on an equal tariff to those who have more than they do."
Top-ups on prepayment meters work in a variety of ways. In some cases they require the owner to take a smartcard or key to a shop. In other cases the owner puts money straight into the meter itself. Some suppliers have recently offered top ups online or over the phone.
But CAP says that when a homeowner is in arrears part of the top up used to pay the debt, so a £10 top up can see just £4 go towards heating.
Mr Barlow told Premier: "We are confident there will be [change].
"Some companies have started to move towards making fairer tariffs available, and we want all the energy firms to follow their lead."
CAP claims that 43,000 people will be unable to afford heating this winter.
It is campaigning for:
- The same tariffs as those on a monthly direct debit - as they pay up to £250 more per year on a pre-payment meter.
- Suppliers to monitor and help families who can't afford to top up
- Better explain the standard charges to customers
- Ensure people on pre-payment meters get the new smart meters first
CAP also hopes that the introduction of smart meters in 2020 will bring greater fairness to the market.
Smart meters calculate exactly how much energy is being consumed by the property, allowing energy firms to provide accurate bills rather than estimating the cost.
Mr Barlow added: "We are asking the energy companies to use the opportunity to do even more to help people who are self-disconnecting because they can't afford to heat their homes."