It all depends on what situation the schools are in- if they have a few NQTs and students already they may not be willing to offer any more experience to people.
The work done by volunteers is mostly group work with children (am basing this on my knowledge of primary schools) reading, playing educational games, cutting things out for displays etc.
I would contact the school directly, have a look on their website first and include a reason why you want experience at their school specifically, e.g. "... your school looks to have very good provision for SEN children, a particular area of interest for me..." in addition to explaining general reasons for seeking experience.