So, here's a build for £5000. Since you live in London, that's kind of the local currency.
PCPartPicker part list / Price breakdown by merchant
This is a bit on the overkill side, but since you have the budget to throw into it, it ought to be. This thing should crunch just about anything you throw at it.
It's similar to what /u/TheReelMVP posted, but I swapped out the motherboard for one with better automatic overclocking features (including the ability to overclock at the press of a button, without knowing anything about it).
I swapped out 64 GB of RAM for 32GB since you're not likely to use more than 32GB ever, honestly.
Swapped out the 850 Pro for the 850 EVO, extremely similar performance for over £100 less. Also, swapped the Seagate Barracuda's for Western Digital's Black series, as the Barracuda has bad reviews and a higher failure rate, whereas the black series is one of the best-rated HDDs around.
I gave you the case you wanted, as well as aftermarket Corsair fans to make the build have better airflow and also be quieter. You also have aftermarket Corsair static pressure fans for your all-in-one radiator, which attaches to the CPU for great cooling.
I gave you aftermarket PSU cables, because it'll look sexy as fuck and also be much easier to work with (they bend much easier), as well as lasting longer.
You also got Windows 8.1, a fast Blu-Ray disk writer, and the Asus ROG Swift, a 1440p 144Hz monitor that has G-sync software that makes everything better. One of the best monitors around.
It's a fantastic build, and you still have money to buy a chair, and your own keyboard and mouse, which are too subjective for somebody over the internet to choose for you.
If you've got the money, don't get an external HDD, get an External SSD like this one. It's got plenty of space for transporting data between computers, and much faster read/write times. Because it's an SSD, it's also much less susceptible to physical trauma, making it a much more reliable external drive than an HDD.
Also, don't get a gaming chair. Get a nice office chair, the quality is much higher and much better priced.
Cheers