Joe - quick answer is :- the small building - I will have to dig out the info that other people have posted. The Furnace Bridge was not a Toll bridge - Info on all the bridges on the river Blyth = https://www.bridgesonthetyne.co.uk/furnace.html
On that site there is info on all the bridges over all the bridges in our area.
The Ha'penny (half penny) Woods did have two Toll houses. One just past the Clock House, on the right of the photo you posted, and one at the entrance to the woods from just over the bridge at the bottom of the Bedlington Bank.
I will dig out some photos.