The technical fault, which was fixed by mid afternoon, affected the CHAPS electronic payment system.
The system is used to move large amounts around the financial system.
It is also used by solicitors at the end of the house-buying process, so some movers were stuck for hours because sales could not be completed.
Bank of England governor Mark Carney said he had launched “a thorough, independent review” into the problem.
“The review will cover the causes of the incident, the effectiveness of the Bank’s response and the lessons learned for future contingency plans,” the Bank said in a statement.
An institution was added to the Bank’s Real-Time Gross Settlement system, which underpins CHAPS, at the weekend.
That created a problem when it was supposed to restart on Monday. It normally operates between 0600 and 1600 on weekdays.
The system was down until about 1600 but a statement suggested all payments should now be processed by the end of the day.
“To help customers and to ensure payments can be processed today CHAPS is extending its operating times until 1940 BST. Customers are advised to contact their own bank for any queries they may have on their specific payments,” said a CHAPS statement.
Among the house movers affected by the system fault was regional manager Laura Baynes, 35, who is buying her first home. She is moving with partner Gregory Trausch and their two dogs, from Horsham to Billingshurst, West Sussex.
“It has taken eight months to get to this point and I am beginning to think I am jinxed,” she said.
Another person affected was Stuart Iles, 46, who is moving with his wife, from Tamworth, Staffordshire, to their new home in Burntwood.
“Our removal firm was here at 8am and we were packed up and ready by noon,” he said.
“But we have been sat on the floor in an empty house for hours.”
There were three buyers in the chain who were all affected, he said. The sale had already been delayed since Friday.
“You expect some problems but this was the last thing we expected,” he said.
“My 10-year-old can transfer money on a smartphone but the Bank of England system crashes when they carry out an update!”
There are about 5,000 homes bought a day in the UK on average, although Friday is the most popular moving day.
The CHAPS system moves billions of pounds every day between Britain’s main banks and building societies. The latest figures show that in 2013 it was used to process an average daily total of 138,000 payments with a combined value of £277bn.
It is used to move money around the financial system, mainly for very high-value payments. It is used for short-term lending between financial institutions, foreign exchange and derivative-related payments. In 2012-13 the average payment was £2.1m, but 78% of payments were below £100,000.
The highest ever settlement figure in one day was for £446bn on 28 September, 2007, during the early part of the financial crisis.
Sometimes it is used by individuals who, for example, want to buy a high-value car and need to make a same-day, guaranteed payment. There is a charge of about £25 or £30 for an individual who wants to use the system, and the payment generally needs to be made by 1500.
Jonathan Smithers, vice president of the Law Society, said: “It is critical for solicitors to have access to this system for house sales and purchases and many other commercial transactions that rely on a payments scheme that processes and settles important and time-dependent payments in sterling.
“We are talking to the relevant bodies to see if we can obtain some understanding of why the system has failed and assurances that this will not occur again.”
Andrew Tyrie, chairman of the Commons Treasury Committee, said: “A crucial part of the UK’s financial infrastructure failed for several hours. I will be writing to the Bank of England to find out why.
“The whole economy depends on a reliable payment system. We need to have confidence that the cause has been found and addressed.”