Santander said it was offering 1 of its shares for every three A&L shares, plus a cash dividend of 18 pence per share. The deal values A&L stock at 317p, compared with a 12-month high of 1,170 pence.
A&L shares soared almost 52 percent to 332.50p after Santander confirmed the deal, reflecting the prospect that a takeover battle could ensue.
Santander shares were gained 1.7 percent, closing at 7.35 euros.
Santander held talks with A&L late last year, sources have said, and analysts said it has the financial firepower to do a deal when many rivals are struggling with the credit crunch.
"It would make perfect sense. If we believe all the reports, before they were looking to buy at above 6 pounds," said Simon Maughan, analyst at MF Global.
He said Santander could use a deal to drive through economies of scale to boost profitability at Abbey, which is low relative to its other operations.
"Even with the cost savings they are planning to drive through at Abbey in the next two to three years, their returns will still be materially less than they make in Europe and a fraction of what they make in South America," he said.
"The merger of A&L with Abbey ... will increase the group's critical mass in the British market," Santander said in a statement, adding that the merged group would have 959 offices and over 8 percent of the British savings and personal loan market.
British rival Lloyds TSB and France's Credit Agricole were also seen as possible predators. Both declined to comment on whether they would be interested.
Entrepreneur Clive Cowdery could also be interested after his attempt to buy a stake in lender Bradford & Bingley last month was rejected, though Cowdery's strategy appears to be to buy stakes and inject capital rather than full takeovers. He could not immediately be reached for comment.