How Can I Develop A Plummy Southern Accent (English?)

Well this depends of course on which accent you are trying to change it from, you don't say which accent you already have and how or why you are trying to improve it or what you are trying to improve it to.

I worked on changing my accent from quite a rough Midlands  (English) dialect to a general standard Southern English for reasons related to my work in the professional theatre.

On the back of my bedroom door, I placed a chart to practice some important vowel sounds:

I wrote Ask Mark to Pass The Glass

In my new accent this sounds like ARSK MARHHK TO PARSE THE GLARSE, rather than the sounds I was producing.

Although the above is not properly written out phonetics, an understanding of phonetics will help you to see how the sounds that you currently are making and the sounds that you want to make are very different.,  

They will also show you want you need to aim for.

Listen to southern accents... Try www.youtube.com Copy what people say