Anyone with children (upto age 16 I think) can request flexible working so I don't think it matters if no-one else in the team has "young" children. I think they probably didn't word their verbal response properly, but it does sound like a "business" reason (it has to be a business reason to reject your request). I guess what they're effectively saying (and no doubt their written reply will be worded better) is that they have to have the same policy for all employees, and the efficiency of the business would be compromised if everyone wanted to work a 4 day week - i.e. there wouldn't be enough cover in the office etc. If thats true, then they probably can refuse on that basis, if not, then challenge it. Good luck.
Yes I wrote in and requested it. Today was the meeting you have to have as part of process, they now have 14 days to officially respond in writing with their decision but that is what was said to me today