Clarkson isn't the only 'celebrity' columnist to have their column removed from The Sun website either and I imagine it is only a matter of time before they get removed from The Times website as well - I'm guessing they'll go for a premium subscription model.
You get most of the site for free but if you pay a few ? a month you'll get all the extra stuff - columnists, crosswords, music downloads, videos etc across all the
News Corp products or maybe just News International Products like The Sun and News of the World (which might be a premium site in itself), The Times and its associated publications (Sunday times, Litery Supplement, Education Supplement, Rich List...).
In fact if you look at the product set as a whole it makes a fair amount of sense - they have ENOUGH premium content to get away with it.