Can anyone recommend a good one?
That's an impossible question to answer without knowing your requirements...
You get what you pay for with hosting. If you sign up for some £4 - £5 per month package, then expect to face a number of limitations further down the line, whether this is no ability to fine-tune your server configuration to suit your ecommerce platform and website requirements or capped limits on database sizes or web space.
What ecommerce software will I be running?
Do I need managed hosting with 24/7 support?
Does my website need or will benefit from a dedicated environment?
How much traffic does my existing website receive?
It goes without saying, that any decent web hosting should be reliable, stable, robust and flexible.
What is your reason for specifying UK based by the way? You want support in UK timezone or you want servers to be located in UK?
We have servers in multiple UK locations, in Amsterdam and in multiple locations in the US. We only offer bespoke hosting packages highly tuned and tailored to individual client requirements with the ability to upscale/downscale with ease as and when needed. We often manage our clients domains at our registrar, look after domain transfers, DNS and mail as well as offer dedicated hosting for our ecommerce clients (I'd go as far as disagreeing with those that say it's best to keep domain separate from hosting - we have an absolute nightmare trying to change nameservers for domains that aren't under our control).
I'd say we're a "good" hosting provider but then, you might require a specific type of server set up that we don't specialise in...