Update, December 2016: the location of the school has been determined.
The location of the school is reported variously as “Orum Alkubra in Aleppo province”, “Awram al-Koubra, outside Aleppo”, “Urm Al Kubra, a village in the Aleppo countryside” and (p7) Urum al-Kubra, south west Aleppo.
In her Independent article of 29 September, Dr Saleyha Ahsan names the head teacher as Mohammed Abu Omar and the school as the private Iqraa Institute. It is referred to as the Ma’jad Iqra’ school on page 7 of this report of The Syrian Human Rights Committee. 
The appearance is of a private residence (note the swimming pool). The toddlers’ swing and a child’s shoe do not match the age of the “students” depicted in Panorama. This Arab language site includes a comment from a contributor said to be from the vicinity of the attack, which describes the building as “a fairly standard construction villa with a swimming pool on the other side of the buttressed wall”.
The BBC’s Editorial Complaints Unit wrote on 23 April 2014 (p10):
My understanding is that the vast majority of schools in Syria have shut down as a result of the ongoing conflict within the country. Many students have not been to school for many, many months. Some private schools have been set up and these are often run from any available premises. In this case I have been informed that the venue was a residential home hired by the headmaster and his colleagues, and they were holding summer courses at the time of the attack
As noted in correspondence with the BBC, an opposition fighter in a video  shot at Atareb hospital on the day of the alleged attack refers to “seven martyrs and about 50 wounded from the religious college for women and girls”. This contradicts the BBC’s account in which the majority of student victims are seen to be adolescent males. I understand that other videos on the same website may contain similar references to a religious teaching centre specifically for females. 
 For observations on “Iqra” schools in Syria see the section “Location of the alleged ‘napalm bomb’ attack (the “Iqra” school)” in my appeal to the BBC Trust of 2 September 2014 and the two reports of the team of local Syrian investigators here and here. Some of the points are summarised and discussed in this more recent post.
 The video in question was originally among those posted on the Free Halab blog. The You Tube channel (“Aleppo and Idleb”) which hosted the video was terminated at some point prior to 8 April 2015.
 It seems questionable whether it would be likely or indeed permissible for a male headmaster (second and fourth images above) and a male teacher to be engaged at a “religious college for women and girls”. Both men’s attire would seem to be incongruously casual for staff of a “religious college”.