While Gillian Shephard has concentrated on building relationships with teachers and their unions, John Redwood, the current challenger to the Prime Minister’s throne, has been talking in terms of a further injection of market forces.

And in apparent response, Prime Minister John Major this week promised to intensify the push for better standards of literacy, for more grant-maintained schools and against trendy ideas in education.

Speaking at the launch of his campaign for next week’s leadership election, Mr Redwood promised that, despite his broad aim of cutting back public expenditure and reducing taxes, the education and health departments would remain spending priorities. He described these as “essential services” and said that “we wish to spend good sums of money on nurses, doctors and teachers - as we have been doing.”

He also announced that he favoured extending the market-driven principle of open enrolment by allowing popular schools to expand further than at present.

John Redwood’s views on education are relatively well known because of his tenure - recently resigned - as Secretary of State at the Welsh Office. This broad portfolio involved running Welsh education.

In April this year, Mr Redwood published a consultation document for the principality’s schools called “A Bright Future: getting the best for every pupil at school in Wales”, in an attempt to raise standards. In the same week, he announced that all 1,800 Welsh primary school would be linked to the Internet computer network in a Pounds 3 million plan, ahead of nationwide schemes launched by the Department of Trade and Industry and the Department for Education.

But some of his initiatives have not been so popular. He had already introduced the idea of passing extra funding to popular schools, who in March were invited to apply for a share of an additional Pounds 23 million on top of the standard financial allocations. This, he said, was to enable them to take more pupils.

He enraged headteachers with a circular linking sixth-form funding to course completion and pass rates.

He also angered religious education professionals by bringing the Welsh RE regulations into line with those in England - a move which involved a greater emphasis on the teaching of explicit Christianity. Mr Redwood is thought to be sympathetic to Christian traditionalists who, since the departure of Baroness Blatch from the Education Department, appear to have wielded less influence over RE and collective worship. Last December he said that “too many of our children are taught more comparative religion than Christianity”.

Some on the left of the Conservative party this week characterised Mr Redwood as a “barking mad right-winger” whose interest in tax cuts is likely to see education coming off second or third best in future public spending settlements.

He appears to have contradicted this with the promise to protect its budget, but critics have been quick to question how long the guarantee would last. His apparent support for the consumer’s right to small schools and small hospitals will be hard to square with tax cuts.

Those on the right of the party feel that for all his ideological zeal, Mr Redwood, a member of All Souls College, Oxford, is more cautious and pragmatic a politician than Michael Portillo.

At the same time they expect a firmer line on standards from Mr Redwood, a former academic and known defender of academic rigour and A-levels. Speaking to a Welsh Grand Committee in February of last year he said, “some teachers think expecting seven-year-olds to read 30 basic words is an unreasonable request by ministers. I have a simple answer: ‘nonsense’.”

Dafydd Wigley MP, president of Plaid Cymru, has suggested that Mr Redwood is as popular in Wales as “a rat sandwich”. But friends warn against taking his abrasive approach towards Wales as a likely model of his future behaviour in mainstream policy-making.

As an avid free-marketeer and sympathiser with the Thatcherite No Turning Back Group, Mr Redwood backs the use of vouchers, currently proposed for nursery education, and is understood to favour their extension into post-16 education. He would like to see more schools becoming grant-maintained, although not on a compulsory basis, and would consider vouchers as a possible mechanism to encourage parents in that direction.

Otherwise, suggest his supporters, he is broadly behind the current line of education policy - on which, they believe, he has already brought substantial influence to bear. Certainly the support he has expressed with Michael Portillo for nursery vouchers and the retention of A-levels has been significant, apparently overriding the wishes of Education Secretary Gillian Shephard.

Bookmakers William Hill put Mr Redwood at 6-1 to be leader of the party by the next general election. Gillian Shephard, felt to be the only candidate aside from Mr Major capable of uniting the party, stands at 10-1.

MPs on both left and right believe that should she be elected, the current low-profile policy would be maintained.

Despite her distaste for vouchers it is thought that a retreat from the current policy of issuing them for nursery education would prove politically too embarrassing to countenance.

With Mr Major placed at 11-10 to retain the leadership, the contenders inspiring the greatest fear will be the two Michaels, Heseltine at 9-4 and Portillo at 9-2. Right- wingers suggest that Mr Portillo’s educational leanings are broadly similar to those of Mr Redwood, although liable to emerge in a flashier, less thoughtful shape.

He is capable of the occasional gaffe; his most recent was the suggestion that Britain is more or less the only place where qualifications are gained on merit rather than through bribery or nepotism. Like Mr Heseltine, he is felt to be an instinctive politician with a sharp grasp of the rhetorical rather than a man who enjoys the nitty gritty of administrative change.

Mr Heseltine himself has rarely forayed into the realm of educational policy, preferring to stick to questions of industry and training. By inclination he is likely to favour a combined, interventionist department of education and training. When asked for his views on schools however, those close to him were able only to point to a section of his prose entitled “small firms’ training challenge”.