BillFlowerpot These days, all gaming-tier graphics cards come with at least one HDMI port, and your TV likely uses HDMI. So it shouldn't be a problem. Nor do you need to spend £2000 or anywhere close to that for the computer itself. Without taking a service contract into account, I should be able to find good options for somewhere in the £800-900 range.
Do you have any preference for the store involved? I know Currys has a number of locations, but perhaps not near you, and maybe you have other stores that are more convenient. Please list any that you're willing to use, and I'll link the best options I find.
As for the software, these systems typically come with Windows pre-installed. For anything else, you'd have to buy a license, but I'm guessing that won't cost another £1000.