You would indeed get more space, but it would involve basically taking the entire roof off the house, building on several more feet to the existing walls and then putting a new roof on.
This will significantly, substantially alter the appearance of your house and you may well not get planning permission for this - in addition to it costing €€€€s. Depends how much extra space you want. Raising the roof like that would enable you to convert more of your attic space because it will increase the useable room (i.e. with sufficient headroom), but you would need to balance how much this'll cost against the amount of extra room you want.
Is there 7.5ft of clearance at the highest point of the roof? That would be enough for a centrally placed room. You could get wide dormer windows installed to increase headroom - planning permission will probably be needed for that.
Another popular solution is to create a full-height room with a flat roof to one side of the roof - usually the part that can't be seen from the road.