I have done as you are prosing to do using parts from Richard Burbidge. There may be other manufacturers, but these people are big and provide lots of options. You buy a new newel and it has a spigot on its base. Its about 50mm diameter and has to be to support the forces involved on the staircase. Burbidge then sell a drill attachment to create the right sized hole drilled into the top of the old newel stub.
Try phoning their technical help line here - I couldn't immediately find in the website that they still do these parts (it was about 15 years ago).
http://www.richardburbidge.co.uk/main.asp?page =62