If you look at your contract it will clarify resignation dates - this is from the NUT website
NOTICE PERIODS AND RESIGNATION DATES
The Burgundy Book national conditions of service agreement for teachers provides that classroom teachers, deputy headteachers and assistant headteachers are under two months' notice and in the summer term, three months' notice, terminating at the end of that school term.
For the purposes of resignations and notice periods, the dates of the three school terms are deemed to be:
· for the autumn term, from 1 September to 31 December inclusive;
· for the spring term, from 1 January to 30 April inclusive;
· for the summer term, from 1 May to 31 August inclusive.
Therefore, teachers who wish to leave their jobs should observe the following deadlines when giving their notice:
· to leave at 31 December, give notice by no later than 31 October;
· to leave at 30 April, give notice by no later than 28 February;
· to leave at 31 August, give notice by no later than 31 May.
It is important to note that these provisions only allow teachers to resign their posts with effect from the end of term
There is no right to leave at half term unless this is mutually agreed by the teacher and the school
I must confess I am surprised you think you can leave mid-way through a term, it is very clear that teachers contacts expect resignations by a set date to leave at the end of a term.