Thanks for your question
As you are engaging this individual to work alongside you then you should be registered for the CIS scheme and thereby making appropriate tax deductions from this gross payment as a Contractor - this will also require the subbie to register within the CIS scheme (as a subcontractor) also.
Its ok when you call upon another skilled tradesman for a couple of hours work to assist with the work as they come along use their own tools, work just for duration of the job requirement, work the hours that suit them, and could make a profit or a loss of the job. So they clearly remain self employed so you can pay them gross. This individual however, works the hours you require from them, they cannot make a profit or loss, and they may well use some of your tools/materials. So they fall within the remit of employment - but through the Construction Industry can just have tax deducted rather than tax and National Insurance (as employees under PAYE do)
You need to get registered as a contractor ready for the next job, and advise all workers that you take on to also get registered as subcontractors, then when they give you their 10 digit unique taxpayer reference (UTR) , you can verify them with HMRC as to what tax deductions you need to make.
You will have to file a monthly CIS300 return and also provide the subcontractors with a payment and deduction statement, detailing your business name and address, your 10 digit UTR, their name and address, the payment date, gross payment and the tax deducted. You then pay them the net amount, and pay the tax deducted over to HMRC (also monthly)
I have added a link here for you to get the ball rolling to register
This also details in more depth your obligations to HMRC.
Do feel free to ask any follow up questions, but if I could trouble you to rate the level of service, I have provided, it would be appreciated, as this ensures Just Answer pay me.