[Build Help] Where do we go from here?

Hey everyone. I've read the rules, and I'm looking for advice, or direction to a resource for people in my situation. I'll explain.

I built a gaming PC around 4 years ago, and it's been a truly faithful servant; however, it's now at the point where it's struggling to meet minimum requirements, and so it's in need of a revival.

I use a 720p HDTV as my primary monitor, and so mega resolutions aren't currently a requirement, though the potential to support 1080p if I was to upgrade the TV in future might be a good call. Don't see myself buying a 4K TV for a while anyway. With that said, I'd like to be able to run games on high/ultra settings at that resolution.

My imminent budget will be around £300; I'm working overtime to generate the income to upgrade, and so it's likely to come in the form of £300/month chunks.

Here is my build at the moment: PCPartPicker part list / Price breakdown by merchant

Where's the best place to start upgrading? Can the motherboard stay, for example, or should the whole thing just get torched and I'll start from scratch? For the record, one of the graphics cards is clearly on its way out, one of the fans is failing and the video outputs are a bit wild.

I'm also getting the occasional system lockups which may be attributable to the RAM. Also, 6GB isn't enough for most games these days.

Please let me know if there's anything unanswered; I'd really appreciate any advice you have.