Detailed guidance for schools on how to assess and tackle security risks is to be issued shortly.
It is likely the money will come through next year's Grants for Education Support and Training programme, which ministers are currently consulting on. Robin Squire, schools minister, told the National Association of Headteachers annual conference in Torquay last week that new money would be found. Afterwards, Mr Squire would not commit himself to a figure, but said: "We will be talking about millions over several years."
The GEST programme is the Government's key way of targeting cash on areas it regards as priorities - it provides 60 per cent of the money and expects local authorities to find the rest.
Early indications are that ministers have been intending to increase the Pounds 263 million GEST fund by Pounds 7m next year, which would just about cover the rate of inflation.
It is understood they are also interested in resurrecting the GEST scheme to provide money for information technology hardware and teacher training, which was scrapped two years ago.
The value of the programme will not be announced until the November Budget but Mr Squire told headteachers: "For the avoidance of any doubt, let me repeat, we will provide substantial new money specifically for school security."
The amount of cash in the GEST fund would have to rise to more than Pounds 270 to represent any real new money for security - any less would mean the cash has been clawed back from other areas. Half of this year's programme is being spent on school effectiveness. Other projects include work on pupil behaviour problems and training for teachers in how to assess the achievements of 11-year-olds.
Local authorities, teacher unions and the working party on school security set up after Mr Lawrence's death have all demanded that money should not be taken from another part of the service.
They have also attacked the tardiness of the Government in delaying finding money for improved school security until next year.
The NAHT called for an immediate injection of at least Pounds 25m from contingency reserves after the working party reported last month.
David Hart, general secretary, warned that schools could not wait and his union's conference last week said panic buttons and mobile telephones should be considered for vulnerable staff.
Education Secretary Gillian Shephard accepted the 22 recommendations of the working party, which were strengthened after the Dunblane massacre. But she said funding had to be considered in the context of wider decisions on public expenditure.
Local authorities are expected to claim later this month that they will need at least a 2 per cent increase on this year's budgets just to standstill in 1997. And the Association of County Councils warned this week that if the increase were limited to a 1.5 per cent rise, as projected, it would be difficult to see how the service could cope with rising costs and pupil numbers.
More than a third of primary pupils are now taught in classes of more than 30 with the pupil-teacher ratio continuing to deteriorate.
Pupil numbers are now beginning to rise in the expensive secondary phase - and spending on special educational needs and exclusions carries on growing.
Also, the ACC said, the introduction of vouchers for four-year-olds would create new uncertainties over primary and nursery budgets.
A joint survey by the ACC and the Association of Metropolitan Authorities has revealed Pounds 3.2 billion needs to be spent simply to keep existing school buildings in use.
Dunblane, page 8