I share 8x57's scepticism regarding the strict legality of issuing a Section 7 permit for this purpose. However I could not be absolutely certain that it is not lawful, I think that it is not. I am not aware of any decided cases (Case Law) that would help.
The reason for my scepticism is that a Section 7 permit may authorise possession (and use) of a firearm and ammuntion, without holding a firearm certificate. However it does not authorise acquisition of a firearm nor ammunition. This aspect is specifically pointed out in Chapter 15 of Firearms Law-Guidance to The Police 2002.
The enigma would appear to be 'how does one use a firearm and ammunition without acquiring it in the first place' ? Borrowing is a form of acquisition.
BASC is a Home Office Approved shooting club. It follows that, where a DSC L1 course is BASC run, on an approved range (with safety certificate etc.) Use without any form of certificate or permit (by a BASC member) would be lawful and this is exemption has been regularly used on such courses, sometimes using club firearms. The question of age, in that case would depent on club rules. Most clubs do not permit persons under fourteen years of age to use full-bore rifles. That is due to considerations, other than the strictures of the Law itself.
Speak with the firearms team at Marford Mill and they should be able to advise where BASC stands on the age aspect in relation to the 'club' exemption.