Well they've got contact addresses for the web designer and the business, which is a start.
However, there's no company registration details in sight and no VAT number.
As it's a commercial website these are key pieces of information that must be included to comply with UK legislation. Full details
here.
If you buy from them use a credit card - that way you're protected. DO NOT used Paypal - you've got NO protection with Paypal IMO.