what is the current area of ventilation required in a room with no external door or window

We would need to know the size of the room to advise on a fan but you can find this information on a search engine by putting in the ventilation required for a kitchen and then look for a site with area vs ventilation requirements. If you can't find a site, then send a rough size of the kitchen and I will try to find out for you.

If this is a question related to the installation requirements for a gas oven/Hob. A Kitchen requires either an operable window or door to outside air. Without that it cannot be installed. There is a gas safe technical bulletin TB005 that covers gas cookers in internal rooms which may list alternative ventilation requirements but i havent read it so not sure what it states.

Unfortunately Fixcookers is incorrect. New directives have been brought in well before they commented stating an openable window or door is no longer needed, and can now be calculated on room sizing alone. You need to employ a gas safe engineer to give you the correct answer