The issue affected customers of telecoms giant BT. The company said that the fault originated with a supplier, Telehouse North, based in London's docklands area.
A BT spokesperson said: "We apologise to those BT customers who had problems connecting to some internet services this morning. Internet usage is now back to normal for consumer and small business customers. A small number of larger businesses may still be experiencing some limited internet access. Engineers should have these fixed soon."
"The issue, which affected BT and other providers, was due to Telehouse North, one of our internet connection partners in the docklands, suffering power issues. The issue affected less than 5% of our customers’ internet usage, and BT took immediate action to minimise these issues by redirecting traffic."
In a statement Telehouse said: "We are aware that there has been an issue with the tripping of a circuit breaker within Telehouse North that has affected a specific and limited group of customers within the building. The problem has been investigated and the solution identified. Our engineers are working with our customers on the resolution right now."
The connection issues on Thursday follow on from similar problems that arose for BT customers on Wednesday "following power issues at one of our internet connection partners’ sites in London", BT said at the time. The company said the issues affected approximately 10% of BT and Plusnet customers' "internet usage" on Wednesday morning but that the problem was fixed services restored later in the day.
According to a report by Finextra, the connection troubles affected users of online banking services from some of the UK's biggest banks.