Plums (particularly Victoria) are highly susceptible to Silver Leaf fungus which is particularly prevalent during mild, wet winters, and enters the plant through pruning wounds or abrasions. This is why plums and cherries should always be pruned in the summer during dry weather, and using tools that have been cleaned and sterilized before and after use.
Check your tree for the following symptoms. Silver leaf causes the leaves to initially gain a silvery hue before browning and dieing off. The shoots will also die back and mauve fungus bracts appear on any dead wood in the autumn. If you can cut off the dead branch that you mentioned and moisten the end of it you may find a dark brown or purple stain within the wood which is also an indicator of silver leaf.
If this is the cause then you will need to cut back any affected growth (in summer, during dry weather), preferably to around 15cm (6) beyond the infected wood. Burn the prunings. I would recommend that you also feed and water the tree to promote its recovery and provide a mulch of well rotted manure or garden compost in the autumn. Take care not to mound any mulch around the base of the stem. If you notice any fungal bracts on the main stem this autumn then it would be best to remove the tree entirely.