This is one of those funny stories which has some truth, but was sensationalised by Thorpe to grab attention.
There's a lot more detail in this post about the original plan, but this picture summarises it nicely:
These are all of the considered locations. There is one location which is essentially next and parallel to Monks Walk (pretty much the back half of Dead Creek Woods and first half of Blair Witch from last year). Obviously not an ideal location. The one next to it would have involved the removal of the carousel and Mr Monkey, and again wouldn't have been great either. Eventually, the current location was decided upon, to obviously redevelop Octopus Garden (an area which was very much out of place at Thorpe).
For some fun bonus info, the park did indeed have South West London Paranormal in (they've visited a few times in the past actually). Jim, who is quoted in the above article, was actually the examiner for my driving test and we spoke about it quite a bit (I also passed my test - woo!). Basically he said there was some stuff detected, some of the stuff he said was obviously used to play along with the story (since there was never any construction in that area, though they did explore the area next to Monks Walk). The group wanted to explore more on different dates, but the park refused, and I don't actually think they've been invited back the the park since..
Funnily enough, that was one of the best, far-reaching, pieces of marketing the park have ever done. It was picked up all over the world, with everyone wanting interviews with the park, wanting to know their next steps, etc. It just really captured the attention and imagination of everyone. And all of that for Storm Surge!
It's why I always feel they should capitalise on the local history and mythology behind it more. The nearby Chertsey Abbey opened in 666AD. There's mythology of a headless monk haunting the town and Monks Walk. It practically writes itself for a dark ride or Fright Nights maze.