One report from the British Broadcasting Corporation said shots had been fired, although this was not confirmed by police. Another report said a bulldozer had been used to tear down the perimeter fence.
A spokesman for the New Millennium Experience Company, which operates the Dome, confirmed that much of the site had been evacuated because of the incident.
Police said they were carrying out a "major operation" which had led to several arrests.
"It is taking place in and around the Dome and there have been a number of arrests so far," a police spokeswoman said.
Initial reports said that four people had been arrested following an attempted robbery on the diamond exhibition being staged at the Dome.
Although it was not clear what was behind the incident, speculation immediately centred on the De Beers diamonds at the Dome, which Sky News reported were the target.
Harry Openheimer, the late former chairman of De Beers and a respected authority on diamonds, once said: "In all my long life I have never seen a more beautiful diamond."
(dpa)