Quite a lot of information on this subject is available on the Internet. You might find online implementations of the formulae given in the annexes, although beware that OS does not check or endorse these. Here are a few addresses directly related to the information in this booklet:
https://www.ordnancesurvey.co.uk/business-and-government/products/os-net/index.html this is the information page for OS Net and contains information and access to data for users of GNSS in GB.
http://earth-info.nga.mil/GandG/coordsys/csat_pubs.html is the US NGA Geodesy and Geophysics department publications page. This has lots of information on the WGS84 datum and the EGM96 global Geoid model.
http://www.igs.org/ is the IGS home page. This gives access to all the IGS products and information about them.
http://www.euref.eu/ is the EUREF home page. EUREF is the governing body of the ETRS89 coordinate system.
http://www.epncb.oma.be/ is the home page of the EPN (EUREF Permanent Network). It gives access details for all EPN data and products as well as information on European reference frames and transformations.
https://www.iers.org/IERS/EN/Home/home_node.html is the home page of the IERS (International Earth Rotation and Reference Systems Service) and gives access to information about the ITRS and ITRF realisations.
Beginner’s Guide to Grid References - Ordnance Survey This guide provides a comprehensive overview of how to use grid references, including helpful tips and a short instructional video.
Here are a few book titles on geodesy, GNSS surveying, and map projections:
Introduction to geodesy: The history and concepts of modern geodesy by James R Smith, published by John Wiley & Sons, 1997.
Geodesy: The concepts by Petr Vanicek and Edward Krakiwsky, published by North Holland 1982.
GPS satellite surveying 4th edition by Alfred Leick, Lev Rapoport, Dmitry Tatarnikov published by John Wiley and Sons 2015
GPS Theory and Practice, 5th revised edition, by B Hofmann-Wellenhof, H Lichtenegger and J Collins, published by Springer-Verlag 2001.
Map Projections: Theory and Applications by Frederick Pearson, published by CRC Press 1990.
Map Projections: A Reference Manual by Lev Bugayevskiy and John Snyder, published by Taylor and Francis 1995.