TSB, Metro Bank, Paragon, and others sent a letter to the Treasury, imploring it to change rules that they said were holding back growth, increasing costs and affecting their ability to lend.
The banks will also meet with city minister Andrew Griffith on Thursday, according to the Financial Times, citing people familiar with the situation.
The lenders will raise concerns about the Minimum Requirement for own funds and Eligible Liabilities regulations, which sets out the amount of equity and debt a bank that has £15.0bn or more of assets or more than 40,000 accounts must hold to absorb losses.
The banks claim that the threshold was too low and disproportionately limits smaller lenders due to the interest costs related to any debt they are required to issue in order to meet the requirements.
The letter said: "As it stands, the UK has been a good place to start a new bank, as illustrated by the number of banking licences granted over recent years.
"However, whilst the barriers to entry have been reduced, the barriers to growth remain stubbornly high, as demonstrated by the fact that no new bank has yet to become a large bank."
The letter also stated midsized banks were "captured by a regime designed for the resolution of large, systemically important banks" and that the thresholds "put UK mid-tier banks at a significant competitive disadvantage relative to counterparts in the EU and US".
Reporting by Iain Gilbert at Sharecast.com