The Metropolitan police commissioner, Sir Paul Stephenson, said today the video images of an officer striking Ian Tomlinson moments before he collapsed and died during the G20 protests in London last week "raise obvious concerns" and should be investigated fully.

His comments come amid growing calls for an independent criminal investigation into Tomlinson's death.

The Independent Police Complaints Commission (IPCC) has appointed the City of London force, whose officers were involved in policing the march and can be seen on the video footage next to Tomlinson, to investigate the incident rather than using its own independent investigators.

The home secretary, Jacqui Smith,defended the role of the IPCC in the inquiry, saying there would be a criminal investigation if necessary.

"What's extremely important from the events last week, from the sad death of Ian Tomlinson, is that there is an inquiry through the IPCC," she said. "If it identifies the need for a criminal investigation, then that also needs to be pursued."

Boris Johnson, the London mayor, is pressing for a "speedy and thorough" inquiry by the police complaints body, his chief spokesman said. He said the mayor watched the footage today and had been seriously concerned by what he witnessed.

Johnson, who is chairman of the Metropolitan Police Authority, is sending his vice-chairman, Kit Malthouse, who is deputy mayor for policing, to meet the IPCC tomorrow.

Many opposition and backbench Labour MPs called for a fully independent inquiry into the attack after the Guardian obtained video footage that showed Tomlinson, a 47-year-old newspaper seller, being knocked to the ground by a police officer in riot gear moments before he suffered a fatal heart attack.

The Labour MP David Winnick, a member of the home affairs select committee, said questions would be asked about "misleading" police statements in the hours after Tomlinson's death.

He said: "One thing is quite clear – the inquiry taking place by City of London police is hardly satisfactory, even if that inquiry is being managed or monitored by the Independent Police Complaints Commission.

"In view of the unfortunate death of Jean Charles de Menezes four years ago, there is all the more reason for concern, which I share, that all the circumstances of this case must be thoroughly looked into. It does seem that the original police statement was, to say the least, misleading in view of what has emerged."

The Liberal Democrat justice spokesman, David Howarth, said: "This video clearly shows an unprovoked attack by a police officer on a passerby. It is sickening. There must be a full-scale criminal investigation. The officer concerned and the other officers shown in the video must immediately come forward."

Howarth described the "shove" by the police officer as "very heavy" and "done with a great force". He told BBC Radio 4's Today programme: "Legally, that counts as an assault. If the consequence of that is bodily harm, then it's a more serious assault; if the consequence is grievous bodily harm, then it's a very serious matter indeed."

The shadow home secretary, Chris Grayling, said the video footage was "extremely alarming" and leaves "big questions to be answered by the police".

He said: "It's right that there should be an independent investigation. The inquiry must be completed quickly so that any further appropriate action can be taken."

The IPCC said it was analysing footage of the attack on Tomlinson provided by the Guardian. A spokeswoman said: "We continue to call for witnesses to the incident in Royal Exchange passage to contact us on 0800 096 9071 or email Tomlinson@ipcc.gov.uk."