No. Apart from the ones you've mentioned, there have been several "one week wonders" this year, so we've already gone way over the record for fewest different number ones in a year.
Not counting 1952, when the singles chart first started (there was just one number one because the chart didn't start until mid-November), the record is jointly held by two years, with the tiny total of just 12 number ones each - 1962 (longest stay at number one: Wonderful Land by The Shadows - 8 weeks, shortest stay: Nut Rocker by B.Bumble & The Stingers - 1 week) and 1992 (longest stay: appropriately enough Stay by Shakespear's (sic) Sister - 8 weeks, shortest stay - Sleeping Satellite by Tasmin Archer and Would I lie To You? by Charles & Eddie - 2 weeks each).
Whitney Houston's I Will Always Love You was number one at the end of the year for a mammoth 10 weeks, but 6 of them were in 1993.