As suggested in a pull request by Edafe Onerhime:

Proposed code: GB-IRN
Title: Department of Education, Northern Ireland
Description: The Department of Education, Northern Ireland issues a unique IRN (Institution Reference Number) to schools in Northern Ireland. The registry can be searched at http://apps.education-ni.gov.uk/appinstitutes/instmain.aspx and includes contact details and statistics for the schools.
Category: GB
URL: http://apps.education-ni.gov.uk/appinstitutes/instmain.asp
Public database: Yes

Proposed code: GB-SEED
Title: Education Scotland
Description: Education Scotland issues a unique seven-digit number to every Scottish school: http://www.educationscotland.gov.uk/parentzone/myschool/glossary.asp#seedno - The registry can be searched at http://www.educationscotland.gov.uk/parentzone/myschool/findaschool/index.asp and includes contact details of the schools.
Category: GB
URL: http://www.educationscotland.gov.uk/parentzone/myschool/findaschool/index.asp
Public database: Yes