A single router might meet your needs - it's really difficult to provide any amount of certainty though.. make sure wherever you buy it from has an easy returns policy, and if you're not happy with the performance, send it back - it'll probably cost you a bit of shipping, but that's a small price to pay 🙂
a £200 router from ASUS is going to be a decent device - likewise from Netgear, Zyxel or TP-Link..
Mesh systems are very easy to manage - they are designed to be plug and play with little effort (but customisation if you're happy to get your hands dirty and know a bit more about networking)
Tri-Band
The TP-Link Deco M9 get's a good write up around here, if you want the wifi-6 variant, then take a look at the X60
Alternatively, if you prefer ASUS, then this AC system has positive reviews, or alternatively, this wifi-6 version
Dual Band
TP-Link Deco M4 & M5 both get positive reviews, as does the x20 (for wifi-6)
You could also buy any asus router that supports their "AI Mesh" technology and if you still have a blackspot you can add any other asus device that also supports AI mesh..