The system, known as Live Restart, is part of the corporation's increasing efforts to improve the live experience on its five-year-old iPlayer service.
Live requests made up of around 22% of all iPlayer requests in April 2012, up by 18% on the same month in the previous year.
Available initially just on PC, Live Restart has some similar functionality to personal video recorder (PVR) services, such as Freeview+, Sky+ and Virgin's V+.
Live TV can be rewound and restarted, meaning audiences do not need to wait for live programmes on BBC iPlayer to end before restarting to the beginning.
With one click on a special Live Restart symbol, users can reload the live programme they are currently watching, or scroll back to watch anything shown in the previous two hours.
"We all know how frustrating it is when you're stuck in a traffic jam, or delayed on the Tube, missing the critical start of your favourite BBC programme," said Dave Price, the head of BBC iPlayer.
"Live Restart solves this by giving audiences control. With one simple click of a button viewers can skip back to the beginning of a live programme, ensuring they never miss a moment of their favourite BBC programmes."
Henry Webster, the executive product manager in Media Services at BBC Future Media, said in a blog post that Live Restart is not exactly the same as a personal video recorder (PVR), as there is no need for users to have been previously watching or recording the show.
"Whenever you join, with one click, viewers can either restart the programme that they are currently watching, or scroll back to watch programmes from the previous two hours," he said.
Webster said that the service is part of the BBC's move to "embrace HTTP chunked streaming for delivering our online video" across all digital platforms.
"Instead of using a point-to-point streaming protocol such as RTMP as we have done in the past, this method breaks up the H.264 video into chunks and delivers them as HTTP packets in much the same way as the we deliver our text rich web pages today," he explained.
"There are a number of reasons why we have taken this approach; firstly it allows us to scale our video operation to a much greater extent than we have been able to before.
"We already use Content Delivery Networks (CDNs) to help us with video delivery, but a move to HTTP streaming means that instead of relying on their capacity to stream video from specialist video servers, we are now able to use their cheaper and more abundant HTTP serving capacity.
"The increased capacity that we can realise this way means that we are more likely to be able to support the ever growing audiences that are turning to their IP connected devices to watch TV and listen to radio."
He added: "This is especially important in a year when we will be streaming more live video to more people than ever before with the Euro Football championships, Radio 1's Hackney Weekend, Wimbledon and the London 2012 Olympics, to name but a few key events."
Later in the year, Live Restart will expand onto the versions of BBC iPlayer on mobiles, tablets and connected TVs, as part of the BBC's strategy to distribute its digital content on as many platforms as possible.
Following its launch on Christmas Day 2007, iPlayer helped bring on-demand TV into the mainstream with a simple and easy-to-use platform that offered catch-up on TV and radio programming seven days after broadcast.
Now available on more than 500 different mobile handsets, tablets and connected TVs, iPlayer also offers live TV and radio channels, along with programme downloads, personalisation features and links to other on-demand sites.