Is it permissible to benefit from, or donate to, the charitable societies, companies, and da'wah organizations in London that are affiliated with the Ash'ari and Maturidi schools of thought?

Helping a Muslim and alleviating their distress is a religious duty. Cooperation with charities run by innovators (ahl al-bid'ah) depends on the nature of their work:

If these organizations propagate innovation (bid'ah), it is not permissible to support them, as this leads to the spread of innovation and associating with innovators. However, it is permissible for someone in need to benefit financially from them, while being cautious not to be influenced by their innovations. If their activities are related to relief efforts or public benefit (such as reform, treatment, or aid), and their administrators are not keen on spreading their innovative doctrines, then the benefit of helping Muslims outweighs the harm of associating with an innovator. If their activities are directed towards inviting non-Muslims to Islam, then supporting them is permissible, because the conversion of a disbeliever to Islam is a great good, even if it is accompanied by some innovations. One should not judge those who administer the organization as innovators if they are ignorant, imitators, or mujtahids who have erred. In summary: Donating to organizations run by innovators is not absolutely forbidden; rather, it depends on the presence of an overriding benefit. However, if there are organizations belonging to Ahl al-Sunnah wa al-Jama'ah that perform the same role, they are more deserving of support.