Tyne and Wear is the most urban part of the North East — Newcastle, Sunderland, Gateshead and South Tyneside packed into England's smallest metropolitan county — so genuine grazing within its own boundary is limited, and much of the horse-keeping happens on smallholdings at the urban fringe. Most families here end up looking slightly further afield into Northumberland or County Durham for wider choice, and that is a normal, sensible approach rather than a compromise.
What the county does have is a large population and a correspondingly active network of riding schools and Pony Club branches serving families who do not have their own land, which is a genuinely good route into ponies before committing to ownership. If you do find a pony kept within Tyne and Wear itself, ask carefully about turnout and space, since city-fringe grazing tends to be tighter than in the surrounding rural counties.