Some Welsh MPs say Mr Clarke's plan, which would exclude non-English MPs from the crucial committee stages, could deprive them of a voice - especially as teachers' pay and conditions are not devolved.
It has also led to renewed calls for full education devolvement to Wales. Elfyn Llywd, Plaid Cymru MP for Meirionnydd Nant Conwy, said some education issues that appeared exclusively English have repercussions in Wales because of this last vestige of power held by Westminster.
Mr Llwyd would like to see a legislative competence order (LCO) passed, enabling teachers' pay and conditions to be determined by Wales. But he is concerned about the Barnett Formula, the funding mechanism through which Wales gets health and education money.
Barnett was introduced in 1978 to give Wales and Scotland a proportionate increase or decrease linked to English public spending. Opinion is split over whether Wales gets a raw deal, and the formula is under review.
It is accepted that the Barnett Formula gives the Scots pound;1,500 per head of population more than in most parts of England. "If we had a proper slice of the cake, we would be more confident in calling for the LCO," said Mr Llwyd.
Gruff Hughes, general secretary of UCAC, the teachers' union for Wales, also wants pay and conditions devolved "at the right time".
Roger Williams, Liberal Democrat MP for Brecon and Radnorshire, is uneasy about Clarke's proposals. "Education and health are mainly devolved but there remain many reserved matters. We would want to be involved in the debates," he said.
Most in-depth amendments are discussed at a Bill's committee stage. "If the Secretary of State is talking about Barnett consequential expenditure - money going to the Assembly - it's the only way we can affect things," said Mr Williams.
"We should have had full devolution in Wales already. We should not have to go cap in hand to Westminster."
However, Mr Clarke's proposals were backed by David Davies, Conservative MP for Monmouth.
"Welsh MPs will still have a vote on the second reading," he said.
Paul Flynn, Labour MP for Newport West, agreed. "It's a pragmatic way of dealing with the situation," he said. "I'd like to see Wales run education. Right now it's a muddle."