The petition, signed by 2,046 people, was submitted two months ago by Ronnie B Financial.
But the government says pricing, terms and conditions of loans and mortgages are commercial decisions for banks and building societies.
It adds that UK Financial Investments Limited manages the public’s stakes in banks on a commercial basis.
It has the objective of protecting and creating value for the taxpayer as shareholder but does not seek to intervene in commercial matters such as pricing or product design.
It says: “Regarding independent advice in the market, the government is committed to promoting understanding of the financial system and raising levels of financial capability across the UK.
“We are committed to improving the advice available to families on how to manage and plan their finances. Once families know how to make sense of what’s on offer, we will make sure that better information is out there on which to base financial choices.
It adds: “We believe that private intermediaries also have an important role to play and that a free national financial advice service will be beneficial to both consumers and the financial services industry as a whole.
“Better informed and more financially capable consumers are better able to engage with the industry and are motivated to take greater responsibility for their financial affairs. In addition, the national financial advice service will be to help individuals to identify when they need regulated advice.”
The petition claimed mortgage lenders are creating unfair price discrimination which limits independent advice and will affect employment and small businesses.