This answer applies if you are made redundant and were paid off. There is no suggestion at the time that the layoff was going to be a temporary and it was intended to be permanent but circumstances have changed.
There is no statutory period which one has to be away from the former employer before being re-engaged but if the employer has any sense, they will have a gap of at least one week. However if there is not a break of at least one week between the previous employment period ending and the beginning of the new one, then notwithstanding the redundancy payment, employment is potentially not continuous and when you start your new period of employment, you do so (if on a employed basis) from day one with no employment rights accrued.
It was a term of being re-engaged, that you repaid the redundancy payment redundancy payment was made subject to repayment if you were re-employed (unlikely unusual) that employment would be continuous and old rights would carry on.
It’s entirely up to the employer whether they pay you are a self-employed basis or not but if you are working hours dictated by the employer and you have no other contracts and you carry no risk and the employer simply sticks the working front of you and tells you what and when to do it, then the revenue may decide that you are really employed and may want you paying tax accordingly through recognised PAYE scheme.
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