Barclays customers have told BBC News that they have had to wait hours on the phone to the bank trying to get applications started.
Some have been told, incorrectly, that their personal details were wrongly entered. Others that having two signatories on their business account is a problem.
Barclays told the BBC that 95% of customers who have applied have received their funds and that it was working hard to help customers who have fallen through the cracks.
Santander told BBC News, “While most applications have been processed quickly and smoothly, some are more complicated and we are working through these as quickly as we can.”
Nearly 270,000 Bounce Back Loans had already been approved for more than £8bn. However, a significant minority of applicants are finding that the funds are hard to get hold of.
A Treasury spokesman said: “Millions has already landed in people’s accounts and lenders are working hard to process and approve all applications as quickly as possible.
“All lenders are welcome to apply to the scheme, and we are working closely with the banks to ensure firms get the finance they need.”