Halifax, which currently owns 606 agencies nationwide, has put 224 outlets up for sale - a move that is expected to save the former building society as much as pounds 50m per year.
The bank said it hoped to minimise redundancies among the 1,500 affected employees by selling as many outlets as possible as going concerns.
James Crosby, the Halifax chief executive, said he had already received numerous expressions of interest, while Countrywide Assured, the UK's largest estate agency chain, confirmed that it was among the potential bidders for the Halifax outlets. Analysts valued the outlets at around pounds 20m.
Mr Crosby said: "It may be easier to sell all the agencies to one buyer, but we are going to be particularly influenced by what is right for our employees. My best guess is that the end result will be a number of groupings as well as some individual sales."
According to Halifax, the move is part of a wider reorganisation initiated by Mr Crosby in December, and the sale of the 224 outlets will enable the bank to concentrate its efforts in the regions where most of its customers live.
Areas where Halifax has a relatively small presence - such as Wales and the East of England - will bear the brunt of the estate agency sales, and a total of 1,500 full and part-time staff will be affected.
Halifax said it was reorganising its current 123 banking and estate agency areas into just 50 "customer marketing" areas, and that a single manager in each area would be responsible for both the estate agency and the banking business.
This would result in some - but not all - estate agency outlets being combined with the banking outlets, Halifax said.
The bank expects to incur exceptional costs of up to pounds 25m from the disposal, and will forego revenues from the outlets of pounds 30m per year for the first two to three years.
The shares closed up 8.5p at 864p.