Lankeela is right. There is no law preventing dogs going into shops or restaurants, although shopkeepers/restauranteurs(sp), etc. are at liberty to refuse dogs in their premises.
I often take my smallest dog under my arm into shops with no problem whatsoever unless there is a specific notice on the door saying 'No dogs'. I will not tie my dogs up outside a shop, ect under any circumstances.
Staff at our favourite pub/restaurant always come out with titbits and a bowl of water for our dogs.