Greensill's founder, Lex Greensill, Bank of England Governor Andrew Bailey and the chief executive of the Financial Conduct Authority, Nikhil Rathi, will also face questions about the collapse of the company and Cameron's actions.
A series of inquiries have been launched into what access lobbyists have had to Prime Minister Boris Johnson's government after questions were raised about Cameron's lobbying for funds.
Haldane - who has struck the most upbeat tone among BoE policymakers about Britain's prospects for a rapid recovery from the COVID pandemic - will step down from the BoE's Monetary Policy Committee (MPC) after its June meeting and start his role at the RSA in September.
"One lesson that we learned from the financial crisis is that withdrawing policy support too early can be very costly," Tenreyro said in an online discussion hosted by Swedish think tank SNS.
"Withdrawing it too early ... can lead to scarring effects on the labour market that would be very costly and slow down growth going forward," she added.
But the price is replacing bonds maturing in 13 years on average with overnight liabilities that would move up in lockstep with a rise in the BoE's policy rate.
"Carolyn has a respected track record built over 20 years at the Bank of Canada and her extensive experience in international financial regulation will be a real asset to the FPC," British finance minister Rishi Sunak said.
The FPC sets capital ratios for British banks and insurers and regulates aspects of mortgage lending, as well as broader financial risks. Its remit does not extend to monetary policy or financial misconduct.
Vlieghe said in an interview published on Monday that the yardstick for Britain's economic revival should not be just a few quarters of fast growth, but a full recovery of its labour market, too.
"My main message is don't think of the Bank Rate being linked to short-term growth in the economy, as that's not enough," he told TheBusinessDesk.com, a regional business news website.
At a time when Brexit is focusing minds on the future of financial services, this is an area of regulatory policy that provides an opportunity for UK financial services to gain competitive advantage on the global stage.
"The speed at which vulnerabilities are remediated should be commensurate with the potential impact that a disruption would cause, and will be an area of supervisory focus," the BoE said.
To support that international work, the Financial Policy Committee will set out in the next Financial Stability Report its view on how a liquidity classification could be developed and an approach for how more consistent and complete swing pricing could be developed in order to promote financial stability.
Swing pricing refers to a charge imposed on investors who want cash back in times of stress.
Wednesday's data from the Office for National Statistics showed that producer prices - which tend to feed through into consumer prices later - were 2.6% higher than the year before in February.
"As I've been saying for months - drawing on the economics of coiled springs, and crouching tigers, and 'Chicken Lickens' - I do think more likely than not we are (set) for a rapid-fire recovery. That is coming, and I think that is coming soon," he said.