Legally, no-one has to acknowledge receipt of it, it's just courteous to do so and gives opportunity to arrange hand over of keys, equipment, etc.
If the staff member tries to retract their resignation and the Council want to accept, this has to be done by resolution at a Council meeting. If the Council doesn't want to accept, it's not obliged to respond in that instance either. A staff member has the right to request a retraction up to the last day of their notice, after which they are out of contract. If the Council want to accept, but can't meet in time, the staff member has to cease work on the last day of their contract and wait until the Council meets. This is because they are technically out of contract and so insurance policies etc won't cover any mishaps. Unauthorised use of computer systems/data protection law also come into play too due to the staff member being out of contract.
If the Council resolve to retract, the staff member is paid basic contracted time for the period spent not working. If the Council fails to resolve to retract, it would be as if the staff member left on the last day of their notice period.
My Council went through this entire process - that's the advice given to us from Citizens Advice, SLCC National Employment Advisor and various articles on legal websites.