David Cameron had convinced himself that by promising a referendum on whether Britain should leave the EU he would help the conservatives win the 2016 elections.
And that he would then be able to steer the party away from that very idea – convince them to vote for ‘stay’.

As you already know, the conservatives did win the elections but Cameron had to throw in the towel. The ‘leave’ campaign had eventually prevailed and now Britain has to deal with that result.

One of the possible consequences being that the House of Lords might prove itself useless.

Most civilized countries are run as democracies and have two tiered parliaments. Sometimes the two chambers have slightly different fields of responsibility. Usually the lower chamber deals with the more mundane issues – money, for instance, while the upper one takes care of the more ‘symbolic’ ones – foreign affairs or the appointment of the Supreme Court Judges in the US. Also the members of the two chambers might get there following different paths.
But whenever a really important decision has to be made both chambers have to agree on it.

Brexit being one of those ‘important issues’.

As you probably know, the members of the House of Lords – the upper house of the British Parliament, are “appointed by the Queen on the advice of the prime minister” for life, not elected ‘by the people’.

Theresa May, the current British PM, seems hell bent to see Brexit through.

The Government will pack the House of Lords with new members if peers threaten to thwart the start of Brexit, The Daily Telegraph can disclose.

Ministers have made clear that they will not allow peers to disrupt the Brexit process by delaying or amending the legislation when they debate it in the middle of next month.

In this very awkward situation, the Tories do not currently control the House of Lords, the present majority in the House of Lords has two options.
Vote their true minds, even if that would mean diluting the kind of Brexit promoted by May or derail it all together. The ‘only’ problem with this version being that it would be perceived as ‘against the will of the people’.
Rubber stamp the bill passed by the House of Commons. Only this would be perceived as either an abdication from the true nature of any ‘upper house’ – to offer a ‘mature opportunity’ to cool off before making a hasty move, or as a proof of cowardice.

Either way, after the Lords will have cast their votes, voices will be heard questioning the utility of the entire institution.

Giving it up, altogether, would be a rather severe blow to the British democracy.
Hailed by the populists, across the left/right divide, simply because it would make matters a lot simpler for them. It is a lot easier to control a unicameral Parliament than a double tiered one – and that is the very reason for which all authoritarian regimes have tried to ‘simply’ their parliaments.
All ‘popular democracies’ – as the communist regimes loved to call themselves – had but unicameral Parliaments. Sitting in very short (bi)annual sessions during which they did nothing but rubber stamping the bills proposed by the government. Just a reminder.

Members of the House of Lords are appointed by the Queen on the advice of the prime minister

Government threatens to create ‘sunset’ peers if House of Lords thwarts Brexit Bill