Possibly. The Employment Appeals Tribunal has made a judgement in a similar case, establishing that the important points are:
- whether there is a contract to perform work or services,
- whether there is an obligation on the person undertaking the work to do it personally, and
- whether the provision of work or services is made in the course of running a profession or business, and the other party is a customer.
In particular the Employment Appeals Tribunal said that tribunals
- must look carefully at any requirement for the individual undertaking the work to do it personally, and
- must evaluate the 'mutuality of obligation' - ie the company's duty to provide work, and the individual's obligation to do it.
If you employ the man with a van on an occasional basis, as and when your deliveries are required, and not always then; and if he has no compunction about turning you down or sub-contracting the work if he is busy, he is obviously much less likely to be considered one of your 'workers' than if he makes regular deliveries for you every Friday, and keeps his Fridays free so he can do them personally.
If you suspect you may have acquired a worker without intending to, take professional advice.