On the review of Saviour's Day, The Guinness Book of British Hit Singles states, and I quote,
"His thirteenth chart-topper and his third Christmas No.1 in a row (including Band Aid II)." (1990).
Mistletoe and Wine (1988) and Savior's Day (1989) were the other 2, making three in all.
His first was in 1960 when along with the Shadows he took "I love you" to number one. He then waited until 1988 for the next with "Mistletoe and Wine". His last solo Xmas number one was "Saviours Day" in 1990.So he has had 3 in total. However as gazzawazza points out he is featured on the Band Aid II version of "Do they know its Christmas" in 1989.
So technically he has had 2 as a solo artist, 1 with the Shadows and 1 as part of a large collective, so 4 in total
Cliff Richard answers this question himself on his Here and Now tour. Initially he says it's two (ie Mistletoe & Wine and Saviour's Day) then says oh yes Bachelor Boy happened still to be No 1 at Christmas.