The £127bn scheme was set up by the Bank in the aftermath of the Brexit vote, and in February closed for drawdowns.
But policymakers feared the end of the scheme could create a shock to the system and alerted lenders to the risk at the end of last year in a seminar, according to a Telegraph report.
Lloyds Banking Group, Nationwide and Royal Bank of Scotland have been among the biggest users of the scheme, each tapping more than £15bn of funding.
Barclays and Santander have also taken more than £10bn from the scheme.
Critics warned the end of the scheme, along with rising interest rates, could usher in an increase in mortgage costs.
However, others noted the TFS had kept mortgage and loan rates artificially low.