Cost of adding a room

I'll give as much information as I can, looking for an idea of the cost, thanks.

4 bed semi, patio doors at the rear that lead directly onto a decking area, this area is mostly shaded so really it's a wasted unused space, the Mrs wants to remove the patio doors & add on another room

The size of the room will be 240 sq ft / 22 sq metres approx

We want to keep the overall height down as much as possible as 1) it's going to be right beside the neighbours & 2) we get good sun from the west in the rest of the garden & don't want to affect that.
The rear garden faces north(ish)

We are considering a couple of steps down into this new room to keep the height of extension down.

Thinking of a roof with a mild enough pitch with a couple of large triple glazed velux windows facing west

Heat wise, considering a multifuel stove only so no plumbing works

Electrically all we need is maybe 4 double sockets, TV point & lighting, I think the easiest way to do this is to run cables externally from the existing consumer unit outside in a conduit to the new room, we want to avoid ripping up floorboards upstairs

Windows & doors facing the rest of the garden (east), considering triple glazing this whole side

I assume we need planning permission?

Traditional or timber frame pros / cons?

If anybody has any ideas as regards the cost of the above or any thoughts generally, I'd appreciate it

Thanks