Lloyds TSB has tabled a £19.8 billion offer for rival banking group Abbey National.
The firm bid follows Lloyds's proposed offer for Abbey last month which the mortgage bank rebuffed.
That bid by Lloyds gate-crashed merger talks Abbey was having with Bank of Scotland.
Mr Peter Ellwood, chief executive of Lloyds said: "Further consolidation in UK financial services is inevitable.
"A combined Lloyds TSB and Abbey National will be a leading player in UK retail financial services and create significant benefits for customers and substantial value for shareholders whilst providing a stronger platform for overseas expansion."
Lloyds says it would keep Abbey's brand and presence on the high street. There would be no Abbey branch closures resulting from the deal for at least two years.
After that, it would begin a programme to bring together Lloyds and Abbey branches in more than 600 places where they were within a quarter of a mile of each other.
Finance union Unifi has called for the Lloyds TSB bid to be referred to the Competition Commission and warned thousands of jobs could be lost.
PA