II am afraid you are over emphasising the importance of committees in a Parliamentary system compared to a Presidential/Congressional one.

In the UK the core of the political system is the executive. Much of the work which is done in the US in committees is dealt with in the UK by the executive.

Take the way the budget is dealt with. The Chancellor of the Exchequer produces his plans and announces them to Parliament. A majority government can be almost certain they will pass into law unchanged. Major changes by the members of the House of Commons would be considered a matter of confidence, passage of which would cause the fall of the government. In those circumstances there could be nothing comparable to the committee consideration which Congress carries out when it receives the President's budget plans.

Subject matter (select) committees have been created in the last generation, but the Committee stage of legislation is either taken in Committee of the Whole House or before an ad hoc committee (confusingly called a standing committee) which just exists with that set of members to consider one bill.

From what I've seen over here (didn't really pay much attention when I lived in the UK), the staff is doing most of the work anyway.  Hundreds of backbenchers with nothing to do but cheer lead leaves me shaking my head.