There is a new facility for tax agents to escalate unresolved PAYE and self assessment queries after 4 weeks. You need to have exhausted the usual channels such as the online due date and the agents’ helpline first but, assuming that you have done that, the new systems should kick in pretty quickly.
In future there will no longer be a need for those with less than £3k self employed income to complete a full tax return. Instead they will make a much simpler submission. This should not be confused with the £1k allowance as tax will still be payable, it is simply the method of notifying HMRC that will change.