@michael
The fact is that nobody knows what the true figure is, though my estimate of up to 40% seems reasonable, given that it corresponds to the percentage of foreign-born people in inner London.
Here's the reply I received from Lewisham Council:
"Dear Dr Whale
Thank you for your email to the Chief Executive.
Unfortunately, we are unable to provide you with an accurate figure for the percentage of social housing currently occupied by foreign nationals in the Borough. The information that you have requested is not available as the Council does not capture this data.
It may be possible for you to make some rough estimates from census data which records whether people were born overseas.
Kind regards,
****
Chief Executive's Personal office"