Can't we just

sack parliament off and replace them with 620 people dragged off the street at random? 

Agreed.

620 is far too many for legislative purposes.

And their constituency surgery role would be better addressed by local Ombudsmen.

The role of communicating Government/Party messages to the electorate has been obsolete since the advent of the wireless

About 100 would be better

"It is high time for me to put an end to your sitting in this place, which you have dishonored by your contempt of all virtue, and defiled by your practice of every vice; ye are a factious crew, and enemies to all good government; ye are a pack of mercenary wretches, and would like Esau sell your country for a mess of pottage, and like Judas betray your God for a few pieces of money.

Is there a single virtue now remaining amongst you? Is there one vice you do not possess? Ye have no more religion than my horse; gold is your God; which of you have not barter'd your conscience for bribes? Is there a man amongst you that has the least care for the good of the Commonwealth?

Ye sordid prostitutes have you not defil'd this sacred place, and turn'd the Lord's temple into a den of thieves, by your immoral principles and wicked practices? Ye are grown intolerably odious to the whole nation; you were deputed here by the people to get grievances redress'd, are yourselves gone! So! Take away that shining bauble there, and lock up the doors.

In the name of God, go!"

- Oliver Cromwell

20 April 1653, London, England

I would totes be up for this and would be more sane (despite my somewhat tenuous grasp on reality) than the majority of the far right MPs.  Or the far left.  Or most of them actually.