In your current situation you get paid for working Tue-Fri year-round with 5 weeks annual leave plus pro-rata Bank Holiday days - so if I have understood you correctly, there being (52x4 +1)= 209 Tue-Fri days in a year, you have (4x5 + 0.8*8) = 26.4 of these days as paid leave. You are on a simple 80% of Full Time contract with fair pro-rata terms. (they may round the 0.4 up or down depending on policy)
If you work Term-Time Only, do you want the flexibility to take an additional day off whenever your child's school has an INSET day? The childrens term time is 190 days (38 weeks a year) but the term dates are 195 days (39 weeks) to allow 5 INSET days within the school's discretion. If you want INSET days then you actually want 14 weeks not-working rather than 13.
The Full Time workers with the same Terms&Conditions are getting a total of 33 days of paid leave and work 228 days each year so have 12.64% of the weekdays in the year as paid leave.
So for you to be employed to work on ( 38 x 5 ) = 190 days per year, the fair amount of Paid Leave you should recieve would be 27.5 days per year (because 12.64% of 217.5 days is the 190 days you want to work)
217.5 out of 261 is 83.333% so yes your annual salary should be about the same under these terms (actually a little higher)
OR they may find it easier to keep you as 80% of Full Time and still have the same total number of working and non-working week-days across the year. You currently have 52 unpaid Mondays and 26.4 Paid Annual Leave days per year. If you ask to be moved to flexible working where you still work the same number of days across the year but have school holiday days off rather than mondays and 26.4 variable days then you will actuall have a handful of extra days to take off over and above the school holiday days which you can use for sports days, school plays etc.
HOWEVER - depending on your role, it might be reasonable for them to refuse this arrangement as this working pattern will essentially enable you to over-ride any arrangements for fair sharing of popular holiday dates among a team if cover has to be provided over Christmas and peak summer weeks. Does your role's workload genuinely vary in line with school termtime dates and would any colleagues be expected to work more in school holiday times to accommodate this request?