I agree with QuattroGirl, the crime rate from my experience in 6 years selling real estate in the area - I haven't heard of any break in's or anything like that with the buyers and sellers of property I have helped in Beckenham. Of course there would be some sort of crime rate, but I always tell people that your house is only as safe as you make it, if you lock your doors & windows etc you are more likely to be safe. If your house looks harder to get into than the houses surrounding it, then it is likely that any people getting up to mischief will look over the home.
The house I purchased in St James had been broken into 8 times in the previous 6 months before I purchased it. 6 of the 8 times it was "broken into", the people walked through the front door because it was left open. Pretty simple, lock the doors and windows and it stops break ins - I havent had any trouble in the year I have lived there.
It may pay to get sensor security lights, crimsafe mesh type security screens and screen doors - but this is with any suburb :)
All reports I have heard is that Beckenham is a great suburb :)