The old-maps.co.uk site has a number of Ordnance Survey maps of the Addiscombe area available which are dated from 1869 to 1939 and in 1:2 500 or 1:10 560 scale. In my most recent usage I found that the site doesn't really work properly in Mozilla Firefox and is a little temperamental even with Internet Explorer (your mileage may vary). Also it is only the 1:10 560 scale maps from 1872 that you can enlarge to actually see anything, the others just give you an idea of what area is covered when you buy a copy of the map.
The site allows 'free maps' to be downloaded and used on personal websites subject to displaying the appropriate acknowledgement text and links so that is exactly what I've done with an 1872 map. I've tried to get a map giving an overview of Addiscombe similar to the Google Map I use on other pages but it isn't quite the same because of the different aspect ratio and the limitations of the scaling. The major difference is that the Shirley Road has been cut off the right hand side, however it was there in 1872.
Image produced from the www.old-maps.co.uk service with permission of Landmark Information Group Ltd. and Ordnance Survey.
The image links to a much larger copy of the map which may help you see more of the detail but I do recommend you visit the old-maps.co.uk site and try it out for yourself.
British History Online also has the same map available and you may find it easier to navigate on that site. The link takes you to a small scale overview of Croydon and you can then zoom in and pan around.
Some of the points of interest that I noted on the map were: