Lord Stevenson, chairman of Pearson and a member of the Economist board, advises Mr Blair on information technology.
The bill will be piloted through by the Crossbencher, Lord Stevenson of Coddenham.
Lord Stevenson, who presided as chairman of HBOS throughout its 8-year existence, is currently a non-executive director at the bookseller Waterstone's.
Lord Stevenson, who presided as chairman of HBOS throughout its eight-year existence, is currently a non-executive director at the bookseller Waterstone's.
Lord Stevenson of Coddenham was chairman of HBOS throughout its eight-year life.
In written evidence to the Parliamentary Commission on Banking Standards, Lord Stevenson also said the bank had become "over-exposed" to the property market.
The report urged regulators to consider banning Sir James, Mr Hornby and former chairman Lord Stevenson from future roles in the financial sector.
His decision not to intervene follows calls for former HBOS chief executive Sir James Crosby and ex-chair Lord Stevenson to lose their titles.
Lord Stevenson was non-executive chairman of HBOS between 2001 and 2009.
Lord Stevenson is currently a non-executive director of the booksellers Waterstones.
BBC: HBOS bosses remain under fire as Sir James resigns posts
If the responsibility for top pay spreads from the boardroom to the annual general meeting, will shareholders accept the arguments made by Lord Stevenson and others?
Lord Stevenson, the former chairman of Pearson, owner of the Financial Times, and HBOS, disclosed only after his retirement that he has had regular bouts of depression.
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Vince Cable wants to see if there is enough evidence to start disqualification proceedings against Andy Hornby, Lord Stevenson and Sir James Crosby, a source told the BBC.
The evidence is in stark contrast to a letter written by Lord Stevenson to the Financial Services Authority in March 2008, just months before the forced takeover by Lloyds.
Shadow culture, media and sport minister Lord Stevenson of Balmacara raised questions about whether traffic and public transport infrastructures would be able to cope with the volume of visitors.
This started life as a private members' bill in the Commons, piloted through by the Conservative, Gavin Barwell, and will be steered through third reading by Lord Stevenson of Coddenham.
"This bill would implement government strategy, " Lord Stevenson concluded.
The issue was also raised by Labour spokesman Lord Stevenson of Balmacara who queried the effect of the law on ticket holders "who cannot for good reason be present at the event".
BBC: London Olympic and Paralympic Games Bill: Second reading
"It is clear that, with the benefit of hindsight, the bank did become exposed to excessive levels of risk, particularly in the wholesale markets and the corporate division, " Lord Stevenson wrote ahead of the hearing.
Halifax chairman Lord Stevenson of Coddenham sale Mr Dunstone had "a very strong media and retailing background" and was "a great fit for an organisation like ours which sees its future in retailing and e-tailng".
The renewed search for individuals to blame for its downfall follows a damning report last week from the Parliamentary Commission on Banking Standards, in which the bank's two leading executives and its chairman, Lord Stevenson, were severely criticised.
BBC: HBOS bosses remain under fire as Sir James resigns posts
The bill, which has been backed by mental health charities and the Royal College of Physicians, builds on the work of Lord Stevenson of Coddenham, who launched a similar bill in the House of Lords in the previous Parliamentary session.
And here is one important reason why the non-bankers on the Co-op's board are nervous about getting bigger in banking: they are acutely aware of how the non-bankers at HBOS, Sir James Crosby, Andy Hornby and Lord Stevenson, were pilloried by MPs earlier this month for making a total horlicks of their bank.
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