The regulations are included in Sections 173-178 of the LGA 1972. In simple terms, allowances are payable by parish and town councils for the necessary performance of an approved duty outside the parish boundary. The sums payable and the procedural issues are, largely speaking, a matter for the council to determine, so there is no obligation on a council to pay anything at all.
The only other form of allowance is the Chairman's annual expenses allowance, covered by Section 15(5). If you are not the Chair, there is currently no allowance payable for the core costs of being a councillor. The NALC has lobbied for a childcare allowance to be permitted, and perversely, the Coronavirus pandemic may accelerate a revision of parts of the LGA to allow this. In the meantime, stationery, ink (or access to a printer), postage etc for individual members could be covered by the Clerk through the council's admin budget.
For attendance at training courses, the cost of the course and the re-imbursement of necessary travel costs should be covered by the council from the training budget.