Having read your article on High Speed 2, whilst visiting family in Sheffield I agree that trains could run from Sheffield to Paris providing that CamdenCouncil agree to the building of a link from HS2 to HS1 through Camden.
At the present time I am not sure that Camden council will play ball.
However, with the electrification of the main line from Sheffield to St Pancras and after some small changes to the layout at St Pancras, refurbished Eurostars could be used to provide a service to Paris utilising Stratford International Station.
Also with new services envisaged from 2015 from St Pancras to Cologne, and Amsterdam, suitable connections could be provided at Stratford for passengers from Sheffield to change trains and enjoy the benefit of high speed train services to many parts of Europe and not just Paris.
Upgrading the existing rail corridors is an often touted suggestion.
However, in the case of the East Coast main line through Retford and Doncaster, I have been informed that at one of the recent franchise option renewals a leading contender expected to bid for the franchise pulled out.
This was because they realised that a new line from London to Peterborough and on to Doncaster would have to be built to provide Yorkshire, the North East and Scotland with a really fast service to London.