It would depend on how you define "fans". They would almost certainly all have heard of it and know a fair amount about it. Most would watch it regularly. As Caitlin Blackwood (who played the young Amelia (Amy) Pond in "The Eleventh Hour", etc.) said, "In this country, you're born knowing about it."
To be quite honest, Doctor Who reached its peak of popularity when it starred Christopher Eccleston and the earliest episodes starring David Tennant. It had a dramatic loss of popularity when Freema Agyeman was cast as the companion Martha Jones, but this was repaired towards the end of the series and it rose in popularity to almost its peak when Catherine Tate was introduced as Donna Noble.
Although the new 11th Doctor series starring Matt Smith and Karen Gillan is fairly popular, it has lost viewers due to the retiring of Russell T. Davies, a popular episode writer and producer of Doctor Who. Many British viewers feel that Doctor Who has lost its 'magic' as a result.