The House of Lords continues to perform an important role scrutinising government legislation. It's membership, predominately experts, ensures that it can properly assess the technical merits of different pieces of legislation. While the life appointment of its members ensures that the Lords is removed from partisanship and sits outside of the narrow debates found in the House of Commons.
Replacing the House of Lords with an elected Senate would run the risk of simply replicating the House of Commons and removing any expertise.
With both chambers claiming electoral mandates, it could lead to the kind of political deadlock that is frequently found in Congress in the United States of America.