They claim to be in the business for 5 years, although I can agree with Trey that their site looks like a mass-produced template.
I found a couple of reviews here: http://www.webhostingunleashed.com/reviews/eukhost-reviews.htm and some more here: http://www.webhostsonline.com/Reviews/E/euk623/index.htm
I found their cusomer service very responsive. During working hours (UK time zone) they usually respond within 20 minutes. No extra charges for listed basic features on top of what they officially claim, I can confirm that. Unlimited domains hosting promise – true too, at least for me.
The next choice pricewise would be easyspace.co.uk – a much bigger hosting company. The cheapest package (1 domain) – 25 pounds/ year, which is still not too bad. They also have more publicity than eUKhost. But they never responded to a couple of my e-mails with questions which discouraged me. I prefer not to deal with companies who ignore customers’ requests (or busy too much to notice little guys?).