I can't really spend more than £500...Projector will be used for films and gaming, ideally I'd have a 4K HDR projector with low noise, but am I best dropping to 1080p considering my budget?
There's no point beating around the bush, £500 for 4K in projection is way off the mark. You need to double the projector budget at least, and even then you're at the very shallow end of the 4K pool.
Before 4K projection was a thing, 1080p projectors from proper home cinema brands ranged in price from £500 to over £50,000. The market broke down something like this:
sub £500 - mostly small portable business projectors - not really suitable for gaming or HC unless you had really low standards
£500~<£800 - gaming and home entertainment projectors - machines tuned for brightness (1500~3000 ANSI lumens) and some with short throw or ultra-short throw lenses for big images at short distances. Pros: good in ambient light, big picture @ short throw distance, reasonably low image lag. Cons: Not great with contrast. Imitated optical sharpness on short zoom models, fan noise, DLP the only real imaging option
£800~£1500 - the overlap between higher-brightness entertainment/gaming projectors and entry-level home cinema (HC) product. HC pros: better contrast, more accurate colour, better motion processing, lower fan noise, start of 3LCD models as an alternative to DLP for those with rainbow sensitivity. Cons: limited brightness 1000-1200 ANSI, requires darker room, optical image sharpness still limited
The above is all still entry-level stuff for the various application categories. There were some key price points above these where performance jumped up. Products such as the 2016/2017 model Epson 7300 at around £2000, and £4000 for the JVC DLA-X5000 set bench marks for performance. At the same time the TV market was streaking ahead with 4K UHD, projectors hadn't really moved on at the same pace. The issue was (and still is) the cost of making true native resolution UHD imaging panels. That's why pixel-shift technology dominates in the current sub £4,000 projector market.
Fast forward to the current projector market and things really haven't changed that much except for UHD pixel shift projectors replacing 1080p at roughly £1000 and above.
The reason why they're not available at £500 yet is a simple one; cost.
The price for the imaging chips is one of the biggest component costs in a projector. One of the most noticeable things about the early generation budget UHD projectors was how the rest of the component qualities dropped in order to accommodate the cost of the new chips. The lenses and video processing and the feature count all took a dip, and I'm not convinced they're back to pre-UHD levels.
Your plan to have a home cinema with a £500 projector that is 4K UHD and does HDR just doesn't stack up. If you can manage to increase your budget then it will help, but I would still look very carefully at the quality of any £1000 UHD projector as I still believe they're compromised because so much of the budget has to go in to the imaging chips.
I will be doing a bit of PC gaming on it too, would text on games like Total War etc be blurry at 1080? Any other considerations I need to think about?
Regarding your gaming; since 1080p projection is just about within your budget do you think it would be possible to set the console or PC to the same resolution. That way there's every chance that the text will be clear. You can always try your console or PC at 1080p resolution on a TV