In a speech to the heads of fee-paying Catholic schools, the Rt Rev David Konstant Bishop of Leeds, also warned against letting unpopular schools "wither on the vine" in open competition for pupil numbers.
"We are facing fresh difficulties, of which the most obvious example is the worrying increase in class sizes across the maintained sector, particularly in primary schools," said Bishop Konstant, chairman of the Catholic Education Service.
"If the only answer to this problem is to forego tax cuts, then I believe we should all be willing to make this sacrifice for the sake of our young people," he told last week's Catholic Independent Schools Conference in Liverpool.
He has been more openly critical of Government education policy than some of his colleagues, notably on opting out which he feels has threatened the community basis of the Church's educational work.
Competition between schools is inherently neither good nor bad, he said. But there should be an element of planning in providing places.
"If this is governed by market forces, some schools will wither on the vine and, while they are withering, the children in those schools will not get a satisfactory education. Planning, even if it involves the closure of some schools, is essential."
* Half of all schools spend less than Pounds 1 per pupil a year on religious education, according to the chairman of the Professional Council for RE. Speaking at the launch of the BBC's five-year schedule of RE programming, Jeremy Taylor called it "a scandalous situation", which the Government is unwilling to address.