The list quoted only gives the 50 most prominent, not all the highest.
Partially the question becomes when is a hill a hill as opposed to a high shoulder of another hill.
Alfred Wainwright identified 214 fells, (now known as Wainwrights) in his series of books (A Pictorial Guide to the Lake District). All but one of these exceed 1,000 feet.
That gives 213 in the Lake District.
https://en.wikipedia.org/wiki/List_of_fells_in_the_Lake_District#Wainwrights
But that list is not exhaustive either as it excludes some hills in the geographical area and includes some as hills that others would exclude.
As an example of the ambiguity, Skiddaw is considered a single hill by Wainwright and Little Man of Skiddaw is also a seperate hill.
On the other hand if one considers the list of Birketts:
(The Birketts are all the Lake District hills over 1,000ft as listed in Bill Birkett's Complete Lakeland Fell), Skiddaw has 4 tops/summits (South, Middle, Main & North) plus North Shoulder. Skiddaw Little man also has the shoulder Lesser Man.
Who is to say which should be excluded and which included?
I have a list extracted from various downloads that shows 605 mountains/hills/summits/tops/prominences of 1000 feet in height in England.
I can list them if anyone should so desire.