Views Tables on Responsive Layout I have a views table block within a panel. 

The table is overflowing the panel and I am trying to understand how to constrain it. I have tried setting it's CSS to various widths but they are always ignored. I can change individual column widths, colours etc but not the width. 

Do views tables ignore these settings and just display to the width of their content?
What is the best way to set their width?

Any tips for using views tables in responsive themes(within panels)?

I'm using Drupal 7.23 , Views 7.37 , Panels 7.33 , Omega-4

Update:
In my CSS for this table I have previously tried setting table {
  width: 100%; (and with !important). I know it is being applied to the table as when I have very colums it increase the width of the whole table to 100% of it's panel.

The problem occurs when there are a lot of columns and the content text of the column is wide. Then the table overflows past 100%. I can make it thinner by changing font size but I am trying to understand how the views table width is set.

In terms of Views table plugins / modules I am looking at FooTable , Responsive Tables and (sandbox) Better Views Tables. None of these are mature modules so I am quite nervous about using them.
Set the table width to 100% with css. If some other rule is overriding this, you may have to increase the specificity or add !important.

If you need more control of your table columns, there is a cool module for responsive tables: https://drupal.org/project/responsive_tables. Haven't yet tried it myself.