flat tappet cam oil?

being the owner of some mid 80s /90 practical bangers -well maintained . hav been reading recently that modrn eng.oils may kill the flat tapets/cam loabs sounds very scary to me as none of our diesels have roller/valves ,how much of a problem is it in the uk is it a problem at all i dont buy AUTO STORE oils as i work for a plant hire co and morris lubes shpd diesel oil is the choice every 5-6000 miles --yes a bit old school but why not i aint payin for it