Tenancy at will - terminable on notice?

Including a clause in an express tenancy at will to enable the parties to terminate the tenancy on, say, seven days' notice would normally be regarded as fatal to the creation of such a tenancy. A recent Court of Appeal case (Katana v Catalyst Communities Housing Ltd [2010] EWCA Civ 370 - an application for leave to appeal heard before one Lord Justice) suggests that it is not. The tenancy in question ran for a fixed term of three months (which, naturally, was outside the 1954 Act because of section 43 of that Act), and then, if the tenant held over, the tenancy was terminable by the giving of not less than one week's notice by either party, regardless of the way in which the rent payable in respect of occupation was either calculated or paid. The tenancy arising at the expiry of the fixed term was, said the court, a tenancy at will. Since the court presumes such a tenancy where a tenant holds over after the expiry of an unprotected business tenancy, and such a tenancy is only displaced by an alternative contractual arrangement made between the parties, such as an express fixed term, or an express or implied periodic tenancy, neither of which were found to exist here, the tenancy continued at will, even though terminable on notice.

This does rather beg the question as to what the "at will" actually means in a tenancy at will. On the one hand, one has always been taught that termination at will means termination now; immediately; at the click of a finger; today. Then again, having the freedom to terminate on notice, but at any time (i.e. not constrained by the special requirements of a periodic notice to quit), still seems to be a form of termination at will. Safe practice is to avoid including such notice periods in express tenancies at will. But maybe the presence of such a clause does not prevent the creation/existence of such a tenancy. After all, what other species of tenancy would the arrangement be?