Unlike the position in the US Congress, there are no permanent, subject based committees in the legislative process. [There are subject based Select Committees - like the Defence Committee or Home Affairs Committee, but they are not (though they could be) used in the passage of a bill.]
The House of Commons website describes the committee stage
"Most Bills are dealt with in a Public Bill Committee.
If the Bill starts in the Commons the committee is able to take evidence from experts and interest groups from outside Parliament.
Amendments (proposals for change) for discussion are selected by the chairman of the committee and only members of the committee can vote on amendments during committee stage.
Amendments proposed by MPs to the Bill will be published daily and reprinted as a marshalled list of amendments for each day the committee discusses the Bill.
Every clause in the Bill is agreed to, changed or removed from the Bill, although this may happen (particularly under a programme order) without debate.
A minority of Bills are dealt with by a Committee of the Whole House (takes place on the floor of the House of Commons), with every MP able to take part."
This website is worth visiting - particularly for the guide to the stages of legislation - which includes videos illustrating the various stages. You can access it here.
There is a more detailed factsheet produced by the House of Commons Information Office which you can read.
