They also fear the committee could be used as a way of avoiding bringing in legislation for regional government.
The move is being seen as an attempt by the government to address MP's concerns that while Scotland and Wales and theoretically Northern Ireland have separate elected bodies, there is no such provision for England.
The Standing Committee on Regional Affairs will have 13 members from English parliamentary constituencies.
It is expected that it would meet in the regions as well as at Westminster.
Leader of the House Margaret Beckett told MPs it was important to "revive" a potential forum for debates for MPs who sit for English constituencies.
It would "also have the capacity for statements to be made from ministers and for questions to be put to ministers", she added.
But the Tories expressed opposition to the plan, saying it failed to address the "West Lothian question" where Scottish MPs can vote on all issues affecting England, while English MPs cannot vote on some issues relating to Scotland which come under the jurisdiction of the Scottish Parliament.
The Tories want only English MPs to be able to vote on issues affecting England.
Conservative MP for Harborough, Edward Garnier, argued that only 13 members would be able to vote on the committee and might be unable to represent the interests of all English regions
Those campaigning for an English Parliament point out that in Greater London, for instance, a population of 7.1m is represented by 74 MPs, compared with 72 MPs representing 5m Scots.
Regional government
The government has attempted to address the issue of Scottish over-representation in Westminster by removing the requirement that Scotland must have a minimum number of seats.
While Liberal Democrats do not oppose plans for a committee for the English regions, they want to see a larger committee with more representation to different parties and regions.
They also fear the committee could be used as a way of avoiding bringing in legislation for regional government.
The approval for a committee by MPs comes amid a campaign to establish regional assemblies all over England.
The Campaign for the English Regions (CFER) draws together those from around England who want their own assemblies similar to the Welsh assembly or the one being set up in London.
It is seeking a commitment from the government for legislation to allow referendums to trigger regional assemblies soon after the next election.
Candidates in London's mayoral elections have raised questions over public spending in Scotland compared to the capital.