The firm - which has its headquarters at Hook in Hampshire - added that it hoped to keep compulsory job losses to a minimum.
'Devastating blow'
"Since we announced the merger with Telewest, we have consistently said that headcount reductions are likely," NTL said in a statement.
"We cannot avoid taking difficult decisions if it means a better experience for our customers in the long term."
Peter Skyte, national officer of the Amicus union, said the announcement was "a devastating blow for thousands of employees across the whole country".
"There is no corporate social responsibility in this announcement and it is difficult to fathom how cutting so many UK jobs will be good for NTL's customers," he added.
On Tuesday, NTL - which has debts of £5.4bn - reported an operating profit of £4m for the first three months of the year, and said it had added 25,800 new subscribers.
Last month, it agreed to buy Virgin Mobile for almost £1bn. It aims to use the brand for all its operations and become the first UK firm to provide a four-way offer of cable TV, internet access, fixed line telephony and mobile phone services.
