Hi Northumberlandlad & welcome to pedelecs

and good luck choosing a bike!
It depends how limited your budget, how steep "not too steep" is - rather different for cycling than driving, and how much or little pedalling you want to do to subsidise the motor power, aswell as your frame size as to which is the best choice for you

but on the face of it a Powacycle may do the job at around £5-600, though I don't know how much peak power it has for moderate or "not too steep" slopes without some effort from you; for higher peak power in the same price range an Ezee Liv is an option, or a Currie Izip (with external rear chain-drive motor, not the hub motor version) would also give high torque for hills (should you need it) with little pedalling and be cheaper too, but I wouldn't say its close to the quality or design of the Liv, which I've ridden, and probably not the Powacycle either, though I haven't ridden one of those.
I saw a Giant Suede for sale in my local Edinburgh bicycles, who have a national chain of stores now (not sure of the nearest to you though if you're in Northumberland, maybe Leeds?

), for £599, but I'm not sure of the peak power or ride quality of it.
If you want to spend more, there's other options

from Wisper, Ezee etc.
A 10 mile round trip shouldn't be a problem at all for most bikes, except perhaps some lead acid battery ones like the currie izip its getting close to their maximum range.
I bought my bike (Ezee Torq from 50Cycles) with a specific "cross city-centre" journey of about 4 or 5 miles in mind, to cut out a 1 hour bus journey, thinking to go further afield out of the city by bike & train, but found it so useful that I now regularly use it for 30-40 mile trips to escape the city within 30-40 mins, get some exercise & explore some of the surrounding area

.
I hope thats useful
Stuart.