David Cameron has warned the country to be braced for "more bad news" after three British people were confirmed dead in the Nairobi terror attack.

Gunfire was reportedly heard from inside the Westgate Mall on Monday morning, where Kenyan Defence Forces are still involved in a hostage rescue operation. Earlier the Kenyan Defence Forces said "most of the hostages" had already been rescued and the majority of the building had been secured in a major military operation.

The UK has offered Kenya assistance, including intelligence co-operation, in response to the attack by Islamic extremists in the upmarket shopping centre which has left 68 dead and more than 170 injured, including many children. Somali-based militant group al-Shabaab claimed responsibility for the atrocity, which Mr Cameron described as an "absolutely sickening and despicable act of appalling brutality".

The Foreign Office is investigating suggestions that a female British terror suspect nicknamed the "White Widow" could have been linked to the plot. It came after reports emerged that a woman was among the attackers, fuelling speculation that wanted Samantha Lewthwaite, who was married to July 7 bomber Jermaine Lindsay, was involved. She is wanted by Kenyan police over links to a suspected terrorist cell planning bomb attacks.

In March 2012 it was reported that Lewthwaite, 29, who is originally from Aylesbury, Buckinghamshire, had fled across the border from Kenya to Somalia.

A Foreign Office spokesman said: "We are aware of the reports and we are looking into them." The spokesman added: "It is really difficult to substantiate. We are looking at the names and seeing what we can find out."

A Twitter account purporting to be an al-Shabaab spokesman named a 24-year-old man from London as one of the gunmen. The @hsm_press2 account listed a string of names it claimed were involved in the attack before being closed down, as previous usernames linked to the terrorist group had been.

The Kenya Defence Forces said it is now in control of the majority of the shopping mall.

One of the Britons killed in the attack has been named in reports as Ross Langdon, who had dual nationality with Australia. The architect reportedly died alongside his girlfriend who was said to be heavily pregnant, Australian media have said. A spokesman for the Foreign Office confirmed that one of the three British people killed in the outrage held dual nationality with the country.

Mr Cameron has said he is returning to London to chair an emergency meeting following the Kenya attack. He tweeted: "I'm cutting short a visit to Balmoral to return to Downing Street to chair COBRA late this afternoon, dealing with the Kenya terror attacks."