Antonio Horta-Osorio came under more pressure after Lloyds Banking Group was hit with a £4.3m fine for failing to pay compensation quickly enough to tens of thousands customers.
The fine is a major blow to Mr Horta-Osorio, who grabbed the headlines when he joined Lloyds as chief executive from Santander in January 2011 by immediately ordering the bank to start paying out to customers who were mis-sold payment protection insurance (PPI). That broke ranks with the other high street banks which had launched a legal challenge against the Financial Services Authority over PPI claims.
Lloyds was already facing investor wrath over Mr Horta-Osorio's bonus for last year, which could reach £1.5m.
The group was by far the biggest mis-seller of PPI, with hundreds of thousands of customers affected. It has already set aside £5.3bn for claims, with reports that this could rise by another £1bn when it reports its 2012 results next week.
On Tuesday the FSA said more than 140,000 customers who were told they were due compensation by the bank between May 2011 and March 2012 were not paid within the 28 days Lloyds had promised. That was almost a quarter of the claims Lloyds accepted in that period.
Some 8,800 customers had to wait more than six months for payment, and almost 25,000 inadvertently dropped out of the process, forcing Lloyds to take action to make sure they were paid. The bank also had no way to make fast-track payments to customers who were left waiting.
Tracey McDermott, the FSA's director of enforcement and financial crime, said: "The industry let customers down badly in relation to the sale of PPI. The significant volume of complaints is a product of [Lloyds'] own failings and the least customers can now expect is that redress, when it is due, will be paid promptly.
"The size of this fine reflects how seriously we view these breaches."
The FSA would not comment whether other banks might face similar penalties for slow payments.
The regulator said the fine also reflected Lloyds' track record. It was fined £1.9m in 2003 for sales of high income bonds; £3.5m in 2011 for mishandling complaints; and £4.2m last year over incorrect mortgage terms.
A Lloyds spokesman said: "When we took the lead in 2011 to compensate customers on PPI, we had not fully anticipated the volume of complaints to be processed... It is important to note that almost all customers who were due redress during the review period have now been paid in full and, as the FSA notes, we have taken steps to ensure customers have not been financially disadvantaged."