Broadcasters look likely to televise more FA Cup matches live, after the Football Association confirmed it was discussing how to end the exclusivity of the current deals that enabled seven betting websites to stream the games to account holders.

The outcry by politicians and campaigners about that arrangement, which makes matches not picked by broadcasters and not kicking off at 3pm on Saturday available on betting websites, prompted the gambling companies themselves to voluntarily give up their exclusivity.

The Betting and Gaming Council, announcing the offer on behalf of the gambling websites – Bet365, Betfair, William Hill, Coral, Ladbrokes, Unibet and Paddy Power – said the companies had not sought exclusivity anyway, and were happy for the FA “or another appropriate body” to show them, so that “the games can be viewed for free by the public with immediate effect”.

The broadcast rights to the FA Cup for 2018-21 are held by the BBC and BT Sport, which have their picks of matches to be televised live, so there was a risk of undermining their audiences if the FA were to show other matches in full, live on its website. On Friday the governing body made clear it was talking to the broadcasters about televising the matches, with a suggestion that any they do not want to show could be streamed by the FA on its website.

A spokesperson for the governing body said: “The FA is in discussions with the BBC and BT Sport, our UK broadcast partners for the Emirates FA Cup, to ensure that every Emirates FA Cup match scheduled outside of the Saturday blocked broadcast hours is now made available to watch live on BBC, BT Sport, or on FA platforms. Further details will be confirmed in due course.”

The FA has barely a fortnight to conclude discussions and organise the live broadcasting arrangements, as the competition’s fourth-round matches start on 24 January. The deals were done with the gambling companies in early 2017 by the marketing giant IMG, which bought the global betting rights to the competition from the FA, before the governing body decided to cancel its then official partnership with Ladbrokes and not enter into any further betting sponsorships.

MPs and campaigners were most outraged by the structure of the deals which made the FA Cup matches available exclusively on betting websites to signed-up account holders, seeing that as a strong incentive for football supporters to be drawn into gambling.