Here is a list I edited down from the Headmasters conference website. I took out anything in West Yorkshire but left all the North Yorkshire and further North and North East. The list is not long and visited most of them as a teenager on many occassions and a few of them since.
NORTH EAST
Ampleforth College
www.ampleforthcollege.york.sch.uk
York, YO62 4ER
Ashville College
www.ashville.co.uk
Green Lane, Harrogate, Yorks HG2 9JP
Barnard Castle School
www.barneyschool.org.uk
Barnard Castle, Co. Durham, DL12 8UN
Bootham School
www.bootham.york.sch.uk
Bootham, York YO30 7BU
Dame Allan's Schools
www.dameallans.newcastle.sch.uk
Fowberry Crescent, Fenham Newcastle upon Tyne NE4 9YJ
Durham School
www.durhamschool.co.uk
Durham DH1 4SZ
Giggleswick School
www.giggleswick.org.uk
Settle, North Yorkshire BD24 0DE
King's School (Tynemouth)
www.kings-tynemouth.co.uk
Huntington Place, Tynemouth, Tyne & Wear NE30 4RF
Hymers College
www.hymerscollege.co.uk
Hymers Avenue, Hull HU3 1LW
Pocklington School
www.pocklingtonschool.com
West Green, Pocklington, York YO42 2NJ
Royal Grammar School (Newcastle)
www.rgs.newcastle.sch.uk
Eskdale Terrace, Newcastle upon Tyne NE2 4DX
St. Peter's School
www.st-peters.york.sch.uk
Clifton, York YO30 6AB
Silcoates School
www.silcoates.co.uk
Silcoates Lane, Wrenthorpe, Wakefield, West Yorkshire WF2 0PD
Woodhouse Grove School
www.woodhousegrove.co.uk
Apperley Bridge, West Yorkshire BD10 0NR
Yarm School
www.yarmschool.org
The Friarage, Yarm, Stockton on Tees, TS15 9EJ
Additional Members of North East Division :
George Stephenson Community High School
Southgate, Killingworth, Newcastle upon Tyne NE12 0SA