DI Graham said Tayside Police has now amassed more than 1100 pieces of evidence — the largest haul gathered in a single inquiry for years — and spoken to more than 100 witnesses.

A HOLMES (Home Office Large Major Enquiry System) team has also been set up at police HQ in West Bell Street.

“We are now working on the biggest investigation in Tayside since the Robbie McIntosh inquiry,” he said. “The Albert Street fire was a big investigation, but in terms of magnitude and evidence gathered, this has become the single biggest inquiry since the murder on the Law.”

Around 24 police officers and staff are working around the clock to track down Mr McBeath’s killer.

In addition to continuing inquiries at the scene and the many interviews that have been undertaken, officers have been reviewing public and private CCTV for eight days.

It is now eight days since Shaun McBeath, a father of two, was found dying in a Hilltown tenement.

Mr McBeath, previously of Arbroath, was found with serious injuries in a flat at about 4.30am last Tuesday, but died a shortly after. He had been at a party in the tenement, between McDonald Street and Rosebank Street.

A number of callers have also passed on valuable information via the anonymous Crimestoppers hotline 0800 555 111.

But a number of other potentially key witnesses have yet to be reached and Mr Graham repeated a plea for them to come forward.

“People should be giving us information, even if they don’t think it’s particularly important,” he said. “They might think it’s trivial, but it could be a vital piece of the jigsaw.”

Although city detectives currently have a range of high-profile crimes to deal with, Tayside Police said they are prepared to work around the clock to make sure Mr McBeath’s killer does not escape justice.

Mr Graham said, “We’re investigating a spate of serious crimes, but we are robust and flexible enough with our resources to be comfortable with this.

“We have a lot of busy periods that don’t necessarily always hit the headlines, and I’d like to think Tayside Police and CID can cope with that challenge.”

Detectives have now traced and eliminated from their inquiries a postal worker they were keen to speak to.

But a man seen leaving the tenement has yet to make himself known, despite appeals. He is aged between 20 and 35 and was seen leaving the close at about 3.50am and heading down the Hilltown.

He wore a light-coloured baseball cap and jacket and had a rucksack and a plastic shopping bag.

Detectives are also keen to hear from a couple walking westwards on Lochee Road, near the former Audi garage, shortly after 4am, with a small white dog, possibly a West Highland terrier.

They also urge a couple seen at Dudhope roundabout, next to the Tayside Police HQ annexe, at 4.26am, to get in touch.

The female has blonde hair and wore dark clothing, possibly with a dark top tied around her waist. The male, who had short dark hair, wore a light and dark striped top, dark trousers or jeans and white trainers.

Anyone who can help the inquiry should contact the police incident room on 01382 591940 or 591941, or text information to 07970 561 546.