Rather Irrelevant, Really.
A number of points spring to mind.
Given the global nature of the internet I'm afraid that no nation can effectively regulate how it operates, given that any nationally - devised Law or Regulation runs out of steam at that nation's border. There is often criticism of the US on El Reg for demonstrating its belief that its legal remit is global, so it would be indefensible to support any other government trying a similar trick.
Facebook (to name but one) is barely answerable to the US government, and it certainly won't be answerable to the UK one; this has been nicely demonstrated by MZ deciding to send a minion to tell the HoC to sod off (which is what it will amount to) rather than doing the proper thing and coming himself. In the specific case of Facebook (although the same argument can be used with other "undesirables") the only real option would be to block its operation in the UK, and I cannot see any government wanting to go down that route for a number of reasons, not least the fact that it would put the UK on a par with (say) NK.
The Consitutional position of the HoL is similarly irrelevant; although I have to admit to having no strong objections to its existence, it is essentially undemocratic, but in and of itself that fact does not preclude its coming up with good policies or policy suggestions. In this specific case it might well come to sensible conclusions that attract the support of many or even most in the HoC, but getting government support is something else entirely.
Even then when it comes to "actual" policy making there is the inescapable disease of corporate lobbying to contend with. Almost by definition corporate lobbying takes place in the shadows unseen by the great unwashed (that includes me, I'm afraid to say) so what emerges at the end of any policy - making process can all too easily be a completely emasculated version of what was originally envisaged, leaving ordinary citizens every bit as vulnerable to being misled, or having their personal data abused as they were before any sort of policy was deemed necessary. No; I don't like it, but I don't think I am under any illusions about things changing for the better any time soon.
Finally (for now anyway) even if the "internet" could be perfectly regulated in the UK (actually it's not the internet that needs any sort of regulation; it's people misusing it that's the problem) that would not prevent misuse taking place beyond the reach of any UK regulation, such as the alleged Russian interference in the US Presidential Election. The abuse could be "processed" elsewhere, but stopping the product of that abuse crossing the UK border would be another matter entirely, not least because the mindset would become one of "we have effectively stopped abuse of the internet in the UK" which in turn would create a misplaced confidence in the belief that as a result no abuse was creeping in (flooding in, more likely) from elsewhere.