Public charitable collections that are carried house-to-house are controlled by the House to House Collections Act 1939 and the House to House Collections Regulations 1947, which established a central licensing regime for such collections. Both statutes are available for download as PDFs on this page, but you are advised to check for any updates or amendments.
As with the Police, Factories etc (Miscellaneous Provisions) Act 1916, which regulates street collections, licences were issued by the police until the Local Government Act 1972, which transferred the licensing role to councils (except in London, where licences are still issued by the police) available here.
Unlike 1916, the 1939 Act specifically states (s11) that a licence is required in order to stage a collection for “money or other property” so there is no ambiguity about whether Direct Debits are covered.
Charities fundraising door-to-door can apply for a ‘National Exemption Order’, which allows them to fundraise without the need to obtain a licence, though they do have to notify a council when they are going to fundraise.
The Office of Civil Society, part of the Cabinet Office, operates the National Exemption Order scheme.
Part 3 of the Charities Act 2006 would have removed the requirement for house-to-house collections (both cash and Direct Debit) to be covered by a local authority licence, but this section was never implemented.
House-to-House collections act 1939