No one has been arrested.

Yesterday, officers were sent to Gilt Chambers on the eighth floor of Far East Finance Centre in Harcourt Road, Admiralty.

The male attacker smashed the door at about 1.45pm and fled.

A witness told officers that the implement used appeared to be an axe.

'The perpetrator did not enter the law firm. He smashed the glass door and then ran downstairs,' a police officer said.

The man, thought to be aged about 20, was about 1.67 metres tall. He was wearing a black shirt and black trousers.

A female employee at Gilt Chambers refused to comment.

Police said the other attack happened on Saturday at the offices of Des Voeux Chambers on the 38th floor of Gloucester Tower in The Landmark, Pedder Street, about 800 metres away from the office of Gilt Chambers.

The attack happened on Saturday afternoon. The office was closed at the time.

It was discovered by a security guard when he found red paint on the wall outside the law firm at about 3.30pm.

After checking closed-circuit television footage, police said the attacker was of medium build and wore a blue-and-white cap and dark clothes.

Another officer said the two law firms had not received any warning before the attacks.

'Up to now, no evidence suggests the two cases are related,' the officer said.

'We are still trying to establish the motive behind the attacks.'

The officer said police would check the closed-circuit TV footage at both buildings to try to identify the two attackers.

The two incidents have each been classified as criminal damage cases and at present are being investigated by two separate teams of crime squad officers.

'If necessary, we will consolidate the two cases for investigation,' the second officer said.

According to police figures, the number of criminal damage cases dropped to 4,515 in the first eight months of this year from 4,609 in the same period last year.

There were 6,807 reports of criminal damage in 2009, down from 6,904 in 2008.