Yeah, all the sites are fine. I've bought from the majority of the UK retailers that are on PCPP. The CPU will come with an included CPU cooler which should have thermal paste pre-applied, or a tube of thermal paste in the box. Usually pre-applied(especially with stock coolers), but some coolers come with a tube of thermal paste, like Cryorig coolers. The case should come with 2 included fans, might only have one though. Either way, it's fine for now. Case fans are easy to add/upgrade in the future and not too expensive, and you're unlikely to be having issues with temps, especially if you're not overclocking. You can easily spend £30-50 on a couple of nice case fans and a nice new CPU cooler when you have some spare cash.
No GPU, it's an APU build so you'll be using the R3 2200G's integrated graphics. Should perform similarly to an RX 550/GT 1030, which is the best GPU you'd be able to fit in this budget anyway, but to do so you have to settle for an 'out-dated'(last generation) dual core from Intel, which is just shooting yourself in the foot. This way, like I said, you can add a low end GPU in the future if you want and you'll be laughing.