A statement, also recorded on its telephone line, said: "We are unable to comment further at this time due to possible legal action against BT."
BT Wholesale said: "Euro1Net has been aware since 12 June that unless we received payment for the outstanding invoices, their services through BT would be terminated.
"We would certainly reconsider our decision to cease the service, but as yet we've had no indication that the invoices will be paid."
The industry regulator Ofcom is investigating the dispute.
Euro1Net, which leases lines from BT, said the telecoms firm had withdrawn its IP Stream service on 21 August.
Customers trying to use the internet are now being redirected to a page explaining that their broadband has been disconnected by BT Wholesale.
Subscription refunds
"We apologise for the disruption that has been caused," said Euro1Net.
"We will in due course be contacting all our customers with details of the refund procedure to claim any unused subscription back."
Euro1Net's broadband service has an annual subscription charge of £120, but some customers would have paid out £240 to be connected for two years.
Ofcom said it was seeking to confirm whether refunds would be available.
It said any customers who paid more than £100 with a credit card might be able to claim from their credit card company.
The regulator is advising people to save all contract and payment details.
Replacement service
Its website said: "Ofcom is closely monitoring developments and gathering evidence.
"We will continue to do all we can to ensure that customers are able to access new broadband services as soon as possible."
Ofcom said people affected would be able to sign up for a replacement broadband service through a new provider from 5 September, but that a dial-up internet service could be ordered immediately.
BT Wholesale said it had to free up lines before customers could order a new service through a different broadband provider.
But Euro1Net claimed the technical processes necessary for lines to be freed up could be completed by 29 August.