* Former chairman Green says bank's reputation 'sullied'
* Green says 'should have drilled into detail'
* Green says compliance has since improved
* Former Lloyds chair plays down Brown role in HBOS deal (Adds further comments from former HSBC chair/ex-Lloyds chair)
By Matt Scuffham
LONDON, July 14 (Reuters) - HSBC should have made deeper checks before buying a Swiss private bank that allegedly allowed customers to dodge taxes and a Mexican business that breached anti-money laundering rules, its former chairman said.
"With the benefit of hindsight, it would have been better to have drilled into the detail much earlier. We didn't get everything right," Stephen Green told British lawmakers on Wednesday.
These scandals have damaged the image of Europe's biggest bank and the reputation of Green, who served as the bank's chief executive between 2003 and 2006 and as its chairman between 2006 and 2010. Green and HSBC had managed to come through the 2007-9 financial crisis relatively untainted.
"We had that reputation sullied by things we didn't get right in a couple of different places," Green told the House of Lords Economic Affairs Committee, which was conducting a one-off session on banking culture.
In 2012, HSBC had to pay a record $1.9 billion fine after U.S. authorities said it had become the preferred financial institution for drug traffickers and money launderers between 2006 and 2010.
"I'm not going to say we covered ourselves in glory because it's not true ... since then they have very substantially reinforced the compliance function and it's clear we needed to do that," Green said.
HSBC's Swiss business has been in the spotlight ever since a former IT employee Herve Falciani fled Geneva in 2008 with files which were alleged to show evidence of tax evasion by its clients. The bank has admitted past failings in compliance and control at its Swiss bank following the allegations.
Green was also asked how he felt about the high levels of pay in the banking industry.
"It certainly kept me awake. [There was] no possible way on moral grounds of justifying it," he told the committee.
The bank's current chief executive Stuart Gulliver, is among the highest paid bankers in Europe with a pay packet last year amounting to 7.6 billion pounds ($11.84 billion).
Win Bischoff, former chairman of Lloyds Banking Group , was asked by the panel about the rationale behind the bank's acquisition of struggling HBOS in 2008. This acquisition has been blamed for forcing Lloyds to seek a 20.5 billion government bailout.
The bank's then chairman Victor Blank said he had been told by then-prime minister Gordon Brown that the deal would not be subject to a competition probe but Bischoff said the decision was not entirely down to political influence.
"It was not done purely because the prime minister encouraged the board of the bank (Lloyds). There had been discussions that this might suit Lloyds very well," Bischoff said. ($1 = 0.6418 pounds) (Editing by Sinead Cruise and Jane Merriman)