In response to the Treasury Select Committee's initial inquiry, Barclays, HSBC and Santander all made a public commitment to continue to provide basic bank holders with unrestricted access to cash machines.
In its report published today - Access to cash machines for basic bank account holders - the Treasury Committee makes clear its intent to write to the other providers of basic bank accounts asking for similar clarification.
Andrew Tyrie MP, chairman of the Treasury Select Committee, said: "Restricting access to cash machines could compromise the network. In certain areas, more than a third of ATMs could be placed at risk if other providers of basic bank accounts were to take similar action or to remove themselves from the LINK system.
"The Committee understands the need for banks to control costs, particularly in these difficult times.
"In this instance, the financial benefits to Lloyds and RBS appear relatively small but those affected would be amongst the most vulnerable people in society.
"The public commitment provided by Barclays, HSBC and Santander to continue to provide basic bank account holders with unrestricted access to cash machines is to be welcomed given the current model for banking and bank charges. I hope other providers will do the same.
"In the longer run, both the way services are offered to customers and the charges they pay need reform to secure greater banking competition."
