The trouble is, to do what you are looking for, abolishing the monarchy, means moving on from focusing on the idea of the royal family being leeches and focus on what system you would put in place to replace the constitutional monarchy we have.
What system would replace it? A system of government like Ireland? France? Germany? USA? Do you want an elected ceremonial head of state, or do you want the head of state to be leader of the government? Is there a better system for the UK, or is a constitutional monarchy the least bad option?
Then there's the issue of getting mass support. Create enough of a groundswell of support that a major political party agrees to put a referendum on its manifesto. Get that party elected to government. It holds a referendum.
How are republicans going to push a "yes" vote over the line? We were promised sunlit uplands from the last referendum... look how well that that's going. How is post-constitutional monarchy UK going to be better for us? There's no £200M a week for the NHS con that's going to do it this time. When people will err toward the status quo, how do you get a majority to vote for change? If it's a no, it'll be put to bed for decades, so this is the one big chance.
And what about other countries with the king as head of state... Australia, Canada, New Zealand, Jamaica etc. Would we be forcing them into a constitutional crisis? Do we just not care about how we impact them?
So, yeah. So far as I can see, grumbling about the royal family will go on as it always has, but I can't see anything actually changing in my lifetime.