A debate in the House of Lords was followed by a vote on whether the House of Lords should be composed of elected members or not.
(to vote a bill ≠ to vote on a bill)
It emerged that a great / a vast / a large majority of Lords opposed an elected upper house.
(to oppose something / to be opposed to something)
Indeed, they argued that an elected House of Lords would create competition between the Upper Chamber and the House of Commons.
Or: Indeed, they contended that an elected House of Lords would cause legislative gridlock.
If the Lords were elected, they would be entitled to the same legitimacy as the Commons.
Were the Lords elected, they would be entitled to the same legitimacy as the Commons.
(If + Preterit é Conditional)
Therefore / as a consequence / consequently, if the Lords were to be elected, it would be necessary to redefine the prerogatives and powers of each chamber.
Some Lords justify the existence of a fully appointed House, arguing that (…)
Finally / To conclude, some Lords assert that the popular will may be expressed in other ways than by voting.
However such an argument may be dismissed (may be discarded), because (…)
One can overlook / reject this argument on the grounds that (…)