Media buying agencies believe that the Sun on Sunday is set to launch "within weeks", but warn of a vicious price and marketing war from rival publishers, and a luke-warm response from cash-strapped advertisers.

Rupert Murdoch told News International staff on Friday that the replacement for News of the World would be coming "very soon", with recent industry speculation pointing to a date of 29 April.

However, one media buying source with knowledge of News International's plans said they understood that Murdoch is now seeking to accelerate the launch timeline to potentially within weeks, with plans for a "roadshow" to advertising agencies being put in place next week.

The insider added that News International is said to be particularly keen to rapidly launch an assault on the Sunday Mirror – one of the biggest beneficiaries of the News of the World's closure – on the basis that the longer it is out of the Sunday market, the more difficult it will be to break readers' loyalty to other titles.

Media buyers have been expecting News International to return to the Sunday redtop market – News of the World shut on 10 July 2011, and a replacement was initially mooted for 7 August to try and capitalise on the start of the Premier League season.

But buyers have been split on the best timing to enter from an advertising point of view.

Opinion has ranged from a swift launch ahead of Easter (April 8), to build up momentum before the April bank holiday, which could disrupt buyer loyalty and dilute the effectiveness of marketing spend supporting the title. Another option is to wait until just after Easter, or even dove-tailing a launch with the start of the Euro 2012 football tournament in early June.

"We always expected it, it is just a matter of timing because as soon as a date emerges, rivals will show no mercy in attempting to shut Murdoch out of the market," said the source. "My understanding is that Rupert has decided to accelerate things and launch it in a matter of weeks."

One newspaper industry executive said one plan mooted last summer – which may easily have been dropped – was for News International to re-enter the Sunday market with a temporary cut price of 50p, and with a base target sale of 1.5m copies.

News of the World, which made annually about £100m in circulation revenue and about £37m in ad revenue, sold 2.66m copies a week before it was closed.

The Sunday national newspaper ad market is struggling, down 17.3% year-on-year in the 12 months to the end of January, some £56m, and if the News of the World is removed the decline in advertiser spend due purely to market conditions is about 11% or £31m.

"So much money has disappeared out of the ad market, and retailers – who have propped up the market – do not really advertise on Sundays so it will be tough," said one media buying agency insider. "There will be a degree of support, advertisers are not adverse to the return of a News International title per se, but the market is stressed."

Enders Analysis estimate that the Sun on Sunday is likely to be able to make between £50m and £100m revenue, which is between about a half and two-thirds of what the News of the World was making.

When NoW closed, rivals cut prices by up to 50%, launched massive promotional campaigns, doubled print runs, and Northern & Shell even launched a new Sunday magazine. News International can expect more of the same when the Sun on Sunday hits the market.

Associated Newspapers, owner of the Mail on Sunday, got as far as printing dummies for a new Sunday tabloid in July last year, although one source believes that it will not revive the project to head off the Sun on Sunday.

Murdoch is likely to receive plenty of support from Sir Martin Sorrell, head of marketing giant WPP, who said in September that he would support the return of a title to the Sunday market.

Sorrell's media buying agencies control 35% of the UK press advertising market – and his media and creative agencies handle all of News International's accounts – which would be a massive boost to Murdoch's plans.

"No Sunday paper has managed to hold on to those big initial reader gains as seen over subsequent ABC periods," said Liam Mullins, head of trading at media agency the7stars. "I don't feel any other title offers the quality celeb gossip or salacious firsts that the Screws did.

"As long as we have seen the end of some of the controversial practices that closed the Screws in the first place, the audience will certainly embrace a Sunday Sun. Advertisers need to be where the readers are and therefore will be supportive of the launch – as it has the potential to do massive numbers."

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