5.6 weeks CAN include bank holidays. It CAN NOT include any days which the employee would not be normally working, so you can't include Mondays.
It is up to you as the employer to decide if you want to include bank/public holidays that fall on a working day (tue-fri in your case) within the 5.6 weeks, or if you want to give those days as extra paid time off.
Can I say something like 14 days (3 full days and a half day on fri) plus all bank holidays which fall on a normal working day?
No because the bank/public holidays that fall on a Tue, Wed, Thur vary year to year. Only Good Friday would be a fixed day of the week. Christmas Day and Boxing Day vary as to the day of the week, as they are specific dates.
If your nanny is working half a day on a Friday, you may be better calculating holiday in Hours rather than days. That way your nanny could take off Fridays if they wished (using say 6 hours) or a Tue/Wed/Thur (using 12 hours).
If your nanny is doing 3.5 days per week, then 3.5 x 5.6 = 19.6 days, which you could round up to 20 days. Bank holidays that fall on those days would be .5 of a day for Good Friday. Xmas and Boxing day (when they fall on a working day - which they will until 2014, when the 26 Dec will be a Friday, so a .5 day).
I am not sure how you get 14 days plus bank holidays, as there are only 4 bank holidays in 2013 that fall on Tue-Fri (New Years Day, Good Friday, Xmas Day, Boxing Day). Thus total of 17.5 days (.5 being the Friday), not 19.6 days.
The holiday entitlement bit of the contract needs to work for all years, not just a specific year otherwise you will have to be changing the contract each year.