I will be pleased to assist you with your question today.
The consultant you take on will not be regarded as your employee for Tax and NI purposes if they are hired as a self-employed person. They will be responsible for ensuring that their own Tax and NI are covered as a self-employed person and will have to confirm their self-employed status to HMRC.
As such, and since they are not your employee, you are not liable to pay minimum wage to them.
The best way to deal with this type of working relationship is through a consultancy agreement securing their position with you. This is a contract between you and the consultant and it should set out the conditions of their work with you along with the percentages they are paid for their work. You can add other arrangements for their working to these documents as they are very flexible. You are unlikely to be able to secure a minimum hourly input from them if they are a pure self-employed person however you can raise this as part of the negotiations with them. If they agree you can insert a minimum working requirement into the agreement with them.
There will be other considerations to bear in mind in such an agreement such as notice periods and the usual covenants against poaching staff and clients, competition with the parent company and, possibly a post employment restriction on where and for whom they work. You will wish to build these into any agreement to ensure that your business is protected in the event that the consultant departs.
If you wish to use this model to take this person on I can provide you with a standard consultancy agreement that I use for my own Company. This will rate as a premium service and I would have to levy an additional charge if you wish to take that forward.
I will understand if you do not choose to use that service, however I should be grateful if you would rate my reply so that I can close off your question and receive my fee for responding.