HI there, in theory, any charity/organisation can scrutinise government policy and recommend reform. Whether the Government chooses to take any notice though is a different matter altogether lol.
Certainly NGOs have done a lot of campaigning on various issues. Take Shelter, for example, they have done so much work on tenancy reform and some of their campaigns (e.g. advocating for the abolition of Section 21 Notices) have actually be successful (that is, if the Government ever follows through on its promise to abolish s.21 Notices - watch this space).
I hope this response has gone some way to address your question.