Also as is often the case in the UK they will probably see their fair share of wet roads. Not being used to how these sort of tyres behave in the wet, will I be fearing i'll slip out if i put the bike over on bends?
Contrary to popular belief, the thread on these slicks won't make much difference, if any.
When riding in the rain, the contact patch with the tarmac is all that matters. On a car or a motorcycle, the water sometimes can't "get out of the way" of the tyre, so it becomes a film between the 2 and causes complete loss of grip. The pattern/thread helps a fair amount by channeling the water outwards, but it won't perform miracles.
However on a bike you usually won't get to those kinds of speeds and you have much more weight per square inch of contact patch, which allows the tyres to push through the water on their own.
As a result, the only thing that matters is how good the tyre grips onto the (soaked and therefore still wet) asphalt.
Softness of the compound is the key, and the City Jets are reasonably soft considering that it's actually a touring-oriented tyre.
A Schwalbe Big Apple or their Super Moto (same as the big apple, but without the puncture protection strip) will provide more grip but will wear out a lot faster. So it all depends on what you're looking for exactly.
as to the part just before your quote : A wider tyre will give more cushioning indeed, at the expense of rolling resistance.