The move comes as ministers continue the Gambling Review, which was launched last December, with Ministers expected to produce a White Paper at the end of this year.
BGC chief executive Michael Dugher said backing a Gambling Ombudsman was further proof of the regulated industry’s determination to drive up standards.
Systems for dealing with customer complaints already exist, but the BGC believes a Gambling Ombudsman would improve the process and make it more consistent for those raising concerns.
The BGC, which represents betting shops, casinos and online operators, is proposing that it should be a legal requirement for all licensed betting and gaming operators to sign up to the new Gambling Ombudsman.
Michael Dugher said: “This is further evidence of the BGC’s determination to drive up standards in the regulated betting and gaming industry.
“We hope that the Government will look favourably on our calls for a Gambling Ombudsman to be established as soon as possible following the conclusion of the Gambling Review, which we strongly support.
“The BGC and its members recognise the need for further change in our industry and a new Gambling Ombudsman would be a step forward in customer redress - I’m proud to be giving it our backing.”
Conor Grant, chief executive of Flutter UK and Ireland, said: “At the heart of our business is a focus on our customers – both delivering great entertainment and making sure that it is always underpinned by increasingly robust safer gambling practices.
"And true commitment to putting customers first also means making sure that they have somewhere independent to go if something does go amiss – that is why Flutter is fully behind the call from the BGC today for the Government to include an Ombudsman in its plans for reform of the gambling industry.”