If he had specific hours and days of work then that could amount to a disciplinary offence, not necessarily n automatic dismissal though. However, persistent misconduct like this could eventually result in dismissal.
As far as notice is concerned, under law, only employees are entitled to receive a minimum notice period in the event that their employment is terminated by their employer. The self-employed do not have the legal right to minimum notice periods on termination.
Whether a self employed worker is entitled to a notice period will depend on their contract. If there is a termination clause that specifies a notice period on termination, the employer would be expected to give that notice if they wish to end the employment relationship.
However, it is often the case that no written contract exists, or there is no notice clause in it. In such situations, the worker can still expect a 'reasonable' notice period to have their employment terminated. This is because even in the absence of a written contract they will be working under an implied common law contract and to terminate such a contract a reasonable notice period is required. The only exception is if the contract was terminated because of gross misconduct, that is any misconduct serious enough to justify the employment relationship terminating immediately.
What is a reasonable notice period will vary greatly and will depend on the individual circumstances, industry practices, length of employment, frequency of payment, etc. There are far too many variables to consider, which means it is usually impossible to give a precise indication as to what would be reasonable in each case. It is therefore down to the courts to make that decision. You can offer him something like a week’s notice as a final offer and he can either take it or leave it and decide himself on how and whether to take things further.