my brother -in-law, through his iphone 5, also cannot access facebook, although I can, via my android phone.
I still can not open either facebook npr BBC pages via my laptop, using chrome or IE.
(This is through cabinet 59, whiteley exchange)
It could be that you are suffering from some sort of congestion at peak times. You should carry out a speed test at different times of the day to see if things change.
Use this speed tester then carry out the further diagnostics this will show your speeds and your IP profile for up and down. If the speed drops but the IP profile stays the same it is probably congestion that is your problem.This test must be done with a wired connection.
The impression I got was that it was streaming that was the problem ie watching sport or iplayer and at peak times, not just specific sites. Obviously if it is just on one or two sites it will not be congestion.