With my having placed several geocaches that are based on the locations that are shown on pictures and postcards of local places, I decided to investigate this address to see how much it has changed. 
A quick look on Google Street View showed that: Number 34 Has Gone! 
See: N 50° 46.307 E 000° 16.976
In fact, this area has changed dramatically from what the old Eastbourne maps show and I was pretty sure why.
Yep!
Way back, during WW2, an uninvited visitor had dropped a blooming great bomb nearby (in fact, a string of bombs) and, subsequently, the area had to be demolished! 
Thankfully, Eastbourne's Roll of Honour http://www.eastbournecousins.com/eastbournerollofhonour.htm does not include any fatal casualties from St. Leonard's Road.