To maybe save all the searching, I'll summarise what I remember from having looked into it myself a bit back.
Yes, it CAN be done. But you have to jump through an awful lot of CAA hoops.
You need quite a lot of hours for a start; either 200 TT or 200 PIC I think, but I'm not sure of that. You have to fill in a horribly long form, saying when and where the flight will be done etc. And you need to give the CAA lots of notice, a minimum of a month I think.
I know this isn't very precise and anyone thinking of doing it will need to look up the details. I'm merely posting it because I was asked by someone who assumed it would be OK, since I regularly took friends flying. They thought it would be the same, and so did I at the time. I then had quite a hard time explaining that we didn't have a month to let the CAA know, apart from anything else.
To most people, it appears to be the same as taking up friends. But to the CAA, you're now in charge of the general public, and that usually means you need a CPL at least. This whole charity flight thing is a BIG concession for them, looked at from that standpoint.
So if you get asked, don't commit yourself before you find out ALL the details.