The sector is already lobbying intensively against draft plans by the Financial Stability Board, the regulatory arm of the Group of 20 economies (G20) to designate funds over $100 billion as systemically important and therefore subject to as-yet undetermined extra supervisory requirements.
Haldane said assets in the fund management sector are currently estimated at about $87 trillion globally and could rise to $400 trillion by 2050 as populations expand and get older and richer.
In Britain, the sector has grown from under 50 percent to over 200 percent of gross domestic product since 1980.
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Haldane said recent trends have seen funds moving into illiquid assets and index-linked, passively managed funds, and away from the traditional actively managed funds in blue chips and government bonds.
"These trends potentially have implications for financial markets dynamics and systemic risk - for example, greater illiquidity risk, correlated price movements and susceptibility to runs," Haldane told the London Business School's Asset Management Conference.
Risks from asset managers are different from banks because they do not provide credit and bear that risk in their portfolios.
"Yet their size means that distress at an asset manager could aggravate frictions in financial markets, for example through forced asset fire-sales," Haldane said.
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Even if the "fail" element in "too big to fail" is a red herring, the "big" is not, he added. The sector has the potential to amplify pro-cyclical swings in the financial system and wider economy, giving a false picture of the price of risk.
Such behaviour could crimp the industry's potential to provide long-term financing to the economy in the form of equity and long-term debt, Haldane said.
"A world without equity is likely to be one with poorer risk-sharing and weaker long-term investment," he added.
Haldane also noted a steady erosion of the industry's direct holdings of British shares, with asset managers de-risking as global equity prices fell sharply during the financial crisis, a time when they could be playing a stabilising role.
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Such behaviour is likely to worsen returns to investors and amplify cycles in the financial system and economy, posing the question of what policy response might be best to deal with risks posed by asset management.
The FSB consultation on asset managers ends on Monday. The sector's mutual funds insist they don't pose risks and point out that none of them failed or caused problems during the 2007-09 financial crisis.
Apart from the FSB work - which mutual funds fear will end with their being required to hold capital like banks - Haldane said central banks have a role too through macroprudential policy, which so far in Britain has focused on increasing capital held by lenders.
Haldane said where the sector's activity poses risks to the wider financial system and economy, then macroprudential policy may be justified even when no leverage is present and banks "are not at the scene of the crime".
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"This is the next frontier for macro-prudential policy," Haldane said.
The sector can also play a role in funding the economy through buying securitised debt, a corner of the market that is still languishing after being tarnished in the financial crisis.
Haldane said there is support for high-quality securitisation products that might comprise much simpler structuring of payoffs and high and transparent underwriting standards.