Firms including NatWest, Virgin, the AA and British Gas have all held talks with BT about the problem, which prevented customers contacting them on freephone and special local rate numbers for more than 24 hours.
Customers were unable to buy goods and services, and in the case of NatWest, some were unable to complete time-sensitive financial transactions - an effect that the bank believes could open it up to claims brought by customers.
A NatWest spokesman said, "Some talks have taken place, and we have sought assurances that the problem won't happen again.
"What we are particularly disappointed about is that it took BT more than 24 hours to get the network up and running again."
He added, "As for compensation, we do have a service contract in place and talks are continuing."
When MCI Worldcom's international frame relay network went down last year, the company almost immediately offered its customers compensation as part of the service contracts in place.
As for the problem on BT's network, a BT spokesman revealed that four networking suppliers helped it to isolate the problem, which was attributable to faulty software on a switch.
When approached by Computer Weekly, three of these suppliers denied that any of their products were to blame, while a fourth refused to comment on the problem. BT will not officially name the supplier whose product was responsible.