Hi
First there is no need for special extinguishers behind the bar or in the cellar. What you usually find are carbon dioxide extinguishers in those areas to cover the electrical risks that exist.
Not knowing the size or layout of the pub, its difficult to say what you need, but a rough rule of thumb is that you need a 13A rated extinguisher (Foam is a good one for that) per 200 sqm of floor space and they should be placed practically around the premises covering the ground floor entrances and exits. Extinguishers under a Fire Risk Assessment can be placed out of the public areas to protect them from being tampered with and damage.
For the kitchen with deep fat fryers, I would recommend a Wet Chemical Extinguisher and also the standard Carbon Dioxide extinguisher for electrical and a large fire blanket.
One thing to remember is if there is a 1st floor, then this also has to be covered with a 13A rated extinguisher, Carbon Dioxide for electrical and a fire blanket in the kitchen area; as this is considered part of the business, even if it is used by just the owners of the pub, as their own private residence.
The place to start is with a Fire Risk Assessment and / or extinguisher site survey.