All you need is a proper invoice (including name and address, company number if a ltd company, VAT number if VAT registered etc etc), from the subcontractor. You are not responsible for their tax affairs, although I always make a point of verifying that a subcontractor who is charging VAT is actually registered for VAT. Fees paid out to subcontractors are accounted for in the same way as any other business costs. So if you charge your client 1,000 and you subcontract the job out for 800, for example, you show a contribution of 200 towards the taxable profits for the year.
It's worth going over this (and any other questions you might have about your accounts and record keeping) with your accountant or other advisor.