Just reading some comments posted about a year or so ago on donating to charity shops. BHF do free collections; however they can be very picky. I have waited in all day for them to collect a mattress; about 2 years old, good condition, no tears, etc. The van drivers were not particularly friendly, and refused to take the mattress due to 'stains'. Apart from it not looking brand new, there were no stains, so not sure what standard it has to be for them to take it. Personally, as I live in a flat, I wonder if they didn't want to bother lugging it down the 3 flights of stairs!
Anyway, I wouldn't bother with BHF unless the item in question is 'nearly new'.