Are they showing VAT on their invoices? If they’re not registered for VAT, they shouldn’t be charging it, so there would be no VAT to recover.
The other possibility, does their charge cover more than just their time? For example, are they incurring other costs relating to the running of the club and charging them on to you? If so, you need to establish who those other suppliers are technically dealing with. If the other suppliers’ invoices are issued to the couple’s company, you cannot recover any VAT. However, if the invoices have been issued to the club and the couple’s company has just paid them on your behalf, you can reclaim the VAT shown on those invoices in the same way that you would have done had you paid the supplier directly.