The BBC’s World Service, whose building is nearby that of the Today programme, also went temporarily off air during the fire alarm.

At 7.40am, an announcer said: “This is BBC Radio 4. I’m afraid we’re having some problems which are preventing us from continuing with our scheduled programme as smoothly as we wish.

“Many apologies for the disruption, but rest assured we are doing our best to restore normal service as soon as possible.”

While the journalists were outside, the station then played pre-recorded interviews, while its website said: “Sorry, we’re having some trouble loading our live shows. Come back soon to try again.”

The show was off air for around 20 minutes until 7.55am, with Robinson’s colleague Martha Kearney announcing the show’s live return by saying: “Alarm over”.

Robinson added: “Despite that noise you may have heard saying there was an emergency, as far as we can tell there wasn’t actually an emergency.

“We have to follow procedures and we did, and we were outside in the cold for a little while but we are relieved to be back on the Today programme. Normal service is being resumed.”