Inspired by the financial success of the Eiffel Tower — which was erected in Paris for the 1889 World's Fair — a group of Englishmen attempted to bang out their own ersatz Eiffel a year later. This contest to design the never-to-be "Great Tower of London" received 68 designs. Some resemble alien fortresses and all of them would've (supposedly) prompted an international Eiffel Tower arms race. To quote:
Taking into consideration the enormous popularity of the Eiffel Tower and the consequent pecuniary benefits conferred on those interested in that undertaking, it is not too much to anticipate that, in the course of a short time, every important country will possess its tall Tower. The project of erecting a great Tower in London soon found the willing support of many capitalists, who felt convinced that if the scheme were properly laid before the public there would be no great difficulty in accomplishing the object.
The pamphlet further elaborated that "the high land between Willesden and Harrow at Wembly Park, has been selected (subject to further consideration)" as a location for this tower. You can see the first two winners — which top out at 1,200 and 1,300 feet, respectively — below, along with some of the zanier proposals. I'm particularly partial to the upside-down screw that is the "Century Tower."
For more monumental weirdness from the 1800s, see the Statue of Liberty in Paris and with a train coming out of her mouth. And for a bird's-eye view from a modern London tower, see the crashing of the Shard.