Wasn't that what was originally planned to be the Home Counties alternative to the Eiffel Tower? Never actually finished and subsequently razed to the ground before the site was in due course re-purposed as the Empire Stadium (= Wembley Stadium).
Exactly that.
Edward Watkin chairman of the Metropolitan, Great Central and South Eastern Railways (in late Victorian times) had this dream of establishing a through route between Manchester, Sheffield, London and Paris and was instrumental in the first attempt to tunnel under the Channel.
His Tower was to be higher than Eiffel's but money (and consequently enthusiasm) ran out after the first stage was built (in 1895). It did remain for a number of years but (as you state) was demolished and the Empire Stadium, Wembley was built and opened in 1923 for the FA Cup Final between Bolton and West Ham. Footie fans will know it as the "Policeman on the white horse" Final.
Rumour has it that the centre circle on the pitch was located precisely at the centre of the tower.
Of course, the Stadium was rebuilt in the early years of this century (I hate it) and I have no idea whether the centre circle of the new pitch corresponds to the old one.
Good article about Watkin on Wikipedia (with a picture of the Tower):
https://en.wikipedia.org/wiki/Edward_Watkin#