First calculate minimum annual entitlement:
5.6 x 40 = 224 hours.
If you work the same number of hours each day, then each day uses 10 hours, so minimum number of days = 22.4
However you are not working the same number of hours per day, as you mention 3.5 days. So look at the hours worked, not days.
Your holiday entitlement in contract is 24 days, so how is that calculated given you don't work the same number of hours per day? Would probably have been easier to state entitlement in hours. Too late now but maybe something to change at a contract review.
"excluding bank holidays" - so does that mean you need to take any bank holidays that fall on a working day as part of your annual leave?
Having worked for 3 whole months, you would be entitled to take up to 1/4 of the annual entitlement. So 1/4 of 224 hours = 56 hours.
In the past 3 months there have been several bank holidays. If those fell on a working day then you may have taken them as annual leave. If they did not fall on a working day, then you can ignore them as they do not count for your holiday entitlement.
December 2013 Bank Holidays:
25 and 26 December. These were a Wednesday and Thursday.
So assuming you did not work them, then as they are on your usual working days you would need to deduct the hours you would have usually worked on a Wed and Thurs from your holiday entitlement.
You have already taken a 3.5 days off... when was that? Was that over xmas and thus already accounts for 25/26 December?
Jan 2014 Bank Holiday: 1st Jan.
This was a Wednesday. If you did not work it, then the usual working hours needs to be deducted from your entitlement.
So hope that helps you work it out.
If you want us to help work it out, we will need to know exactly how many hours you work on each day and if those hours are the same every week.