London's mobile phone networks face a "capacity crunch" during the Olympic games that could leave the capital and its expected 1 million extra visitors unable to use the internet on the move unless thousands of wi-fi hotspots are built in time.

Virgin Media chief executive Neil Berkett, whose company is bidding for council contracts to build a central London public wi-fi network, believes the process is moving too slowly and fears the Olympics could be a "missed opportunity".

His comments come days after London mayor Boris Johnson warned that the mobile phone service would come under "massive strain" at peak times during the games.

Berkett said: "The mobile networks are already facing a capacity crunch that, without widespread, consistent wi-fi, will leave people unable to do the most basic things such as keeping up to date with the latest travel situation and getting directions while out and about."

Use of the mobile internet is growing at speed, along with adoption of smartphones, and that is already putting pressure on networks, with Three mobile warning that it will run out of capacity on some masts by the end of 2012.

Wi-fi is cheaper and faster than 3G internet, and most mobiles are programmed to switch from phone masts to wi-fi where it is available. The hope is that it will absorb a swath of web traffic during the Olympics and beyond if a substantial network can be built in time.

Westminster city council has shortlisted six bids for a long term contract to build a borough-wide public wi-fi system and is due to announce a winner in November. Virgin Media has made the shortlist, along with O2, BSkyB's wi-fi business The Cloud, BT Group and two smaller companies. It is understood Kensington & Chelsea has committed to adopting the same supplier as Westminster, and Hammersmith and Fulham is expected to follow suit. Virgin is keen for other central boroughs including Southwark, Islington, Lambeth, Hackney and Camden to do the same.

Even if the public wi-fi network is built on time, it is unlikely to offer equal access to all users. While it will be free to everyone, there will be speed and time limits for those who are not customers of the winning bidder. Virgin, for example, could offer its customers speeds up to 20 times faster than guest users. One bidder is understood to want to impose a 15 minute a day limit on internet time.

Virgin is offering to build an outdoor network, with transmitters hung from lamp posts and bus stops every 80 to 100 meters at thousands of sites in central London. O2 and BT will build predominantly indoor networks, in restaurants, pubs and cafes.