A fourth British soldier has been killed on operations in central Iraq, the Ministry of Defence has confirmed.

As American forces began a full-scale assault on the rebel city of Fallujah, one member of the Black Watch was killed in an area north of Camp Dogwood.

Initial reports said a roadside bomb was involved in the incident, which also injured two others, one possibly seriously.

Reacting to the news, a Downing Street spokesman said: "Our thoughts are with the Black Watch battle group and their families after this incident."

Meanwhile, a former senior foreign policy adviser to Tony Blair has expressed his doubts over the legality of the invasion of Iraq.

Sir Stephen Wall told Chatham House that "in Britain, we allowed our judgment of the dire consequences of inaction to override our judgment of the even more dire consequences of departing from the rule of law".

In Fallujah US forces launched a huge onslaught  - with 15,000 Marines and soldiers pushing ahead with Operation Phantom Fury.

The new offensive comes as a Populus poll for the Times finds that support for the war in Iraq has fallen to just 31 per cent.