For WordPress shared hosting (the most basic and affordable level of hosting available, suitable for start-ups, small blogs, and low traffic websites), my top recommendation is:
For UK based hosting, I recommend the following:
TSOHost (you can get a 10% one-time discount using this coupon code: KATSO10)
For professional WordPress web hosting, I recommend managed hosting with the following hosts:
Please note that affiliate links are included in some cases. Hosts are chosen purely based on services offered.