To start the story of our edifice, a few things need sorting out.
Properly it’s Tilbury. Although known as Tarner Tower, The Tower was built by Edward Tilbury. This plaque (a bit painty at the moment) inside the Tower attributes the building of the Tower and laying out of the garden to him in 1836, although some documents indicate the house and garden to have dated from 1810. The start of the Tarner association dates from 1836 when Edward’s daughter Lettitia married Edwin Adolphus Tarner. That the tower, park and surrounding neighbourhood bears the Tarner name, rather than Tilbury, is another story…
2. Timothy Carder was WRONG!! (*awaits lightening bolt*) As anyone who has considered the history of Brighton will know, Carders ‘Encyclopaedia of Brighton’ is one of the key reference works. Here is what is has to say re our favourite structure:

Clearly this is not our Tower. We do not have 70 steps. What was Mr Carder on about then?
It turns out there were TWO Towers! Although having a perfectly serviceable Tower in his new garden built by his father–in-law, the young Edwin decided to build his own, bigger, better tower just up the hill. Apart from reflecting on what Freud might have made of all this, had Freudian analysis been around at this time, this also raises a further question: What happened to the other Tower?
The Sussex Daily News in 1941 published this photograph. It is of Tower House, built at the top of Sussex Street, having 70 internal steps and a grand sea view. The reporter records …”It was because of the sea that Tower House was built. One good soul named Edwin A Tarner was responsible for its erection…”
The newspaper entry continues with the viewing ships at sea story which Carder attributed to the Tower in the park, and some of the confusion clarifies as it is apparent that the two structures have become conflated and intertwined over time.
Concluding the item the reporter comments “Strange there is little recorded about Edwin A Tarner …I have approached many prominent townspeople now well on in years, but my story has been pieced together from what I have been able to collect from the old folk in this back part of Brighton, an area speedily disappearing. I hope they will allow Tower House to remain” Sadly it was demolished in the 1960’s.
Tracking a story back 200 years in a changing community has its challenges. The brief foray above shows that even the best documented and most reliable sources, concerning the most high profile residents are full of holes, assumptions and confusions.
Best of luck to us I say!