Old Geezer has a point. Unfortunately the more complicated a tree is then the more you need to be sure of what's what by buying the certificates. However, there's an outside chance that the 1939 Register on FindMyPast might help here. You can get a list of Palmers and Cartwrights in Leeds in 1939, but it will help enormously if you have some idea of ages etc
There were three other David W Palmers born in Yorkshire at this time (1943, 1947 and 1948) any of whom may have married in 1968.