It could be that they are not VAT registered, if it is a very small restaurant with a low turnover, or a new place that has not reached the £79K compulsory registration threshold.
Otherwise, they must be VAT registered, must charge VAT on restaurant food, and must give you a receipt showing their VAT number etc.
Many of the raw ingredients will be zero rated for VAT, so VAT can not be reclaimed where it has not been collected in the first place. People who moan about having to pay VAT bills do not grasp the principle of it; it is Value ADDED tax; it is added onto the price that they are charging; they are simply adding it to their prices, keeping it till the end of the VAT quarter, and then handing it over to HMRC (less the VAT they have paid on expenses). Essentially they are acting as a tax collector.
RE Pete's comment - "the owner does not like to give out his VAT number"... utter bollocks - he is legally bound to show it on receipts / invoices - nobody can use it for anything anyway.... unless they wanted to pay hid VAT liability
