Mr Cameron is on a four-day tour of India

The minibus was travelling on the Great Eastern Expressway in Mumbai when it struck the young woman at about mid-day local time (0800 BST).

Journalists in the bus and UK Deputy High Commissioner Vicki Treadell had earlier asked the driver to slow down.

Mr Cameron and shadow chancellor George Osborne were in separate vehicles.

'Unfortunate accident'

The woman, named Prema Naik, was taken to the KEM Hospital in Mumbai, where doctors do not expect her to survive.

Mrs Treadell said: "This was a very unfortunate accident, which we deeply regret.

"We did what the law requires, which is to go to the local police station and report it."

I was shocked and saddened to hear about this dreadful accident David Cameron

She said the driver, called Samson, and a police officer had claimed in their statements that the woman had "run out" into the traffic.

"They braked, but not quickly enough," she said.

The entourage had been en route to the Taj Mahal Hotel for a lunch appointment following a trip to a slum.

After the incident, a group of angry people reportedly gathered around the minibus and Samson was hit several times in the face, suffering cuts and bruises.

A police officer attempted to calm the situation before the minibus could be driven away to a police station.

Compensation claim?

Samson and the police officer made statements before the minibus went on to the hotel.

In a statement made after the crash, Mr Cameron said he was "shocked and saddened to hear about this dreadful accident".

"It involved a High Commission vehicle carrying journalists, members of my staff, and members of the High Commission staff," he said.

"I know that the High Commission is cooperating very closely with the police to assist them in their investigations, and the High Commission will also do all that it can to assist the victim and her family."

Mrs Treadell said British authorities would pay "due compensation if that's appropriate".

Tax cuts 'secondary to stability'

Mr Cameron's Indian tour has already included opening a �15m JCB plant in Pune with company chairman Sir Anthony Bamford.

Sir Anthony's donations to the Conservative Party, through an organisation called the Midlands Industrial Council, have prompted Labour chairman Hazel Blears to ask the Electoral Commission to reveal if any other donations have been received by the Tories from that organisation.

Mr Cameron accused Labour of muckraking, adding that the Midlands Industrial Council had given to the party in the past, and that the Electoral Commission was "very happy with the arrangements".

He also told BBC Radio 4's Today programme that he believed economic stability would come before tax cuts under a Tory administration.

He was responding to claims by Tory ex-Cabinet minister John Redwood, also head of the party's policy review on economic competitiveness, that higher growth came from tax cuts and that lower taxes drove success.

Irish example

Speaking from India, Mr Cameron said: "If you have a choice, then stability must come first. Over time we will lower taxes because we will share the proceeds of growth.

"But I don't think it makes sense to make big promises about up-front tax cuts. I have said that's an approach we have taken in the past, a process I don't think is sensible."

But Mr Redwood told Today: "Lower taxes drive success.

"Look at the way Ireland has grown three times as quickly as the UK as a whole and four times as quickly as highly-taxed with high public spending Scotland over the Brown years."