Unlike with bikes, you can save yourself a lot of monies by buying the parts and building it yourself. You also have the opportunity to spend hours pouring over different parts and tinkering (which for me is half the fun).
I’ll steer clear of recommending any parts, as I’ve been out of the loop for a few years. There will be plenty of build guides on places like ‘Tech Radar’ for different budgets.
Lastly, £1000 will buy you one hell of a PC. Mine cost more like £600, and is still powerful enough to run any of the latest games. I’d reserve some of your budget for a good quality screen and peripherals, as someone else mentioned above.