from the question I understand that you are not a British citizen as british do not need a visa for Korea. you will need to check if Korea asks for a transit visa for your specific citizenship - if they do not then you will be allowed to get on the flight as long as you can present the second flight ticket towards your final destination.
as to the luggages: if the second flight is operated by the same company or a partner company the transfer is done usually automatically by them and you should not have any problem. i suggest you check with the airline company as there are some airports in the world whent they can not do this (happened to me once or twice)
however, if they are different companies and you are required a Korea visa then you are in trouble as lugagge colection is after passport control, so you will not be allowed to go through.
Hi,
Thank you so much for your reply.its the different companies unfortunately :(. Actually I am travelling together with a German national. Can he check out get out luggage and check in again with my passport while I wait in the transit area ( no transit visa needed in Korea). Will the airline at should korea lets him check in for me as well just with my passport? Thanks