We have an unelected head of state and an unelected upper house of parliament. Now I'm quite conservative on the head of state thing but the upper chamber we have now is a joke.

The method of electing the lower chamber is also not great but it's democratic, of a fashion.

So, how would you change it, root and branch? It's easy to spout rhetoric whilst not having any real ideas. I am genuinely interested to know what and how you would change.

House of Lords replaced by a directly elected body of say 300. Elected on fixed, six year terms, with 100 being up for election every two years. They can run for re-election only once and would represent 10 broadly similarly-sized geographic areas on a proportional representational basis (i.e. 10 get voted in each election from each area).
The chamber would inherit from the Lords its powers of oversight and scrutiny which would be reinforced with more powers on areas of governmental misconduct and enforcing constitutional norms (if we must persist with the latter system rather than an actual written constitution). The lower house remains the main legislative arm of government but the upper house ensures the laws being passed are well-written, workable and stand up to constitutional scrutiny.

I’d like to see a proportion of ‘Lords’ appointed by lottery, similar to jury service. For the rest, I’d happily get behind Ghost’s suggestion.

Pretty much what I had in mind. A limited number in the House of Lords, on a fixed term. What are we at now? Nearly 800? Ridiculous.

In the Economist's ranking of democracies (Democracy Index) the smaller Nordic countries occupy most of the top places. However, Canada (7th) and Australia (9th) are also ahead of the UK (14th) - so clearly there are examples out there that we can learn from.
We should also try and minimise/ eliminate any interference from non UK organisations and individuals. Anyone who has seen the recent documentary series about Murdoch must surely be appalled at the hold he has had over UK politics for the last 40 years or so - and now of course we have Russian funding of political parties.
Politics has always attracted some pretty questionable characters, but in recent times it has definitely got worse rather than better.

The head of state has no power it is purely ancient history and keeps the tourists coming. The house of lords is a joke and needs disbanding or it needs to reduced to 100 previous senior MPs.

As for elections they are as democratic as they come - you can argue against first past the post and argue for proportional representation - the fact that every adult has a vote and they can vote for whoever is prepared to stand in their ward makes it democratic - what more do you want? Other than have only Labour allowed to stand?