A 25% stake in TSB is to be floated on the stock market next month, owner Lloyds Banking Group has announced.
Lloyds confirmed the job losses, but said 65 new roles will be created across group operations and retail.
A statement said: "Lloyds Banking Group is committed to working through these changes with employees in a careful and sensitive way. All affected employees have been briefed by their line manager today.
Compulsory redundancies will always be a last resort. In fact, since the strategic review in 2011 around only a third of role reductions have led to people leaving the group through redundancy."
Lloyds said that of 15,000 previously announced job losses, 13,055 will have gone after today's news.
The Unite union has said it will press Lloyds Bank for a guarantee of no compulsory redundancies as the banking group was revealed to be axing 645 jobs and closing a telephone banking centre in Warrington.
Over 2,400 jobs have gone at the taxpayer bailed out bank since the start of the year leading to "plummeting" staff morale, said Unite.
Half the job losses half will result from the Warrington site's closure by the end of 2014, in a move Unite branded as "unjustified" and a "bad deal" for customers. Most of the other cuts will be from the group's wealth business and HR function, said Unite.
Lloyds Bank is to axe 645 jobs and close a telephone banking centre in Warrington, the Unite union has said.
As the government confirmed it has sold more of its stake in Lloyds Bank, ITV News Business Editor Joel Hills looks at what that means for the tax payer and the company:
UKFI says overnight it raised £4.2 billion by selling more of the taxpayer's stake in Lloyds. Got 75.5p/share, market close yesterday 79p.
Our stake in Lloyds has fallen to 24.9% - in the City when a company owns 25% of another company it is deemed a controlling shareholder.
UKFI is a company with HM Treasury as its sole shareholder which is mandated to manage the Treasury's shareholdings.
Government has sold 7.8% of shares in Lloyds Banking Group, at 75.5p per share.
Govt stake in Lloyds now less than 25%. Part of our long term economic plan to deliver economic security
The government is planning to sell more of its stake in Lloyds Bank, ITV News Business Editor Joel Hills reports.
Another slice of our stake in Lloyds to be sold overnight. UKFI hopes to raise £4.2 billion + reduce taxpayer holding from 32.7% to 25%
There's a picture emerging of a nervousness across the finance sector north of the border, after Lloyds and Barclays warned that a vote for Scottish independence may carry risks and costs for them.
There was even talk emerging today of Lloyds and RBS having to move their headquarters south in the event of independence.
That's because it seems there is an old European diktat that says a finance house must be headquartered where most of its customers live - in both those cases, that would be in England.
So that would be bad news potentially for jobs in Scotland, and bad news certainly for the prestige of Edinburgh as a major finance hub.
However, George Osborne has warned in the past of a bloated finance sector that Scotland couldn't support in the event of a financial crisis.
But if their headquarters weren't in Scotland, it wouldn't be their problem - it would be England's.
So as ever on this topic, there's more than one way to look at any of the issues that emerge.
Barclays bank has warned that the upcoming vote on Scottish independence could "affect the group's risk profile" by potentially destabilising financial markets.
Barclays' warning follows concerns expressed by several other financial institutions about the effect of the independence vote, including Lloyds Banking Group, RBS and Standard Life.
Barclays said: "The referenda on Scottish independence in September 2014 and on UK membership of the European Union (expected before 2017) may affect the Group’s risk profile through introducing potentially significant new uncertainties and instability in financial markets."
Barclays said the vote could bring uncertainty "both ahead of the respective dates for these referenda and, depending on the outcomes, after the event".