Last time I went in to Newcastle it cost (IIRC) £57 for about 4 hours parking, landing and handling (off a VFR approach). My 'plane is 1734kg MTOW so presumably the charges would be lower if you're flying something lighter.
Taxi to the city centre was about £25, I think, although I could be a bit out there).
XL319, where is "Durham" ? Do you mean Fishburn ?