, arguing that students would be "distracted" and teachers underprepared if the gadgets were rolled out on a large-scale basis now. Bungled wholesale introductions of tablet computers to schools in the US should serve as a warning to Britain, he added.
However, Mr Harrison insisted that the government would be forced to look at introducing tablets across the board, "possibly during the next parliament", in a bid to overcome the widening "digital divide" between the best- and worst-resourced schools.
His comments coincide with research showing that nearly four in 10 students admit they are addicted to their mobile phones and tablet computers.
"If [education secretary] Michael Gove was to turn around and say he had the money to hand every student their own tablet, I would say don't do it," Mr Harrison said. "It would be a disaster.
"We still have to put in the groundwork [to get one-to-one tablets right] and put together a proper blueprint. If we did it now, we would have kids distracted, teachers confused and the computers wouldn't be used properly."
His comments are supported by recent events in the US, where so-called "one-to-one access" to tablets has gone wrong. The most high-profile failure occurred in the Los Angeles Unified School District, the second largest school district in the country, which agreed a $1 billion (pound;590,000) deal with Apple to give each of its 640,000 students an iPad.
Problems plagued the initiative from the start, including students hacking the devices to surf the internet and download games. The district then prevented students from taking their devices home after parents voiced concerns that they would be forced to foot the bill if the computers were lost or damaged. It has since been forced to slow the roll-out of the scheme.
Such situations should serve as a cautionary tale, Mr Harrison said. "You only have to look at the introduction of electronic whiteboards. There is a serious white elephant there," he said, referring to early teething problems when the technology was introduced. A lack of training meant that they were not used or merely became glorified overhead projectors.
So far, ministers have left procurement decisions to schools, but Mr Harrison believes that pressure will continue to grow on the government to provide personal tablets for pupils in order to even out inequalities.
However, Miles Berry, principal lecturer in computing education at the University of Roehampton and board member of UK ICT subject association Naace, argued that such decisions should continue to be made at school level, adding that allowing pupils to use their own devices could be a cheaper option.
"Economically, targeted support for `bring your own device' solutions seems far more sustainable than public sector procurement of hardware, which sometimes seems designed with its own obsolescence in mind," Mr Berry said.
In a survey commissioned by charity Tablets for Schools, 39 per cent of more than 2,200 pupils aged 11-17 said they were sometimes addicted to their smartphones or tablets. Some added that they felt "nervous", "angry" or "paranoid" when they were without their devices, while others said they were concerned about their often "compulsive" checking of social media.
The Department for Education responded to Mr Harrison's comments by stressing that it was down to individual schools to decide whether to introduce tablets "based on their pupils' needs".