There may be other options but from the top of my head I can only think of one "simple" solution as the local block isn't an entity in it self but a part of the page  - add the action to the page's controller.

If the block can also be used a shared block, meaning you want the action in the block's controller you could implement the action in the page's controller to just delegate to the block controller's action.

Thanks, as I am using a block controller and my own view model to extend block properties I have passed page content guid to view and used an html 5 data tag for ajax request back to action and load the page info again, this works but probably not the best solution

e.g.

var pageRouteHelper = ServiceLocator.Current.GetInstance<PageRouteHelper>();
if (pageRouteHelper.Page != null)
{
PageContentGuid = pageRouteHelper.Page.ContentGuid;
}

Same problem here, I want to filter a block with ajax, any suggestions other than adding an action to the page controller? 

Set up Web API and use that instead for AJAX requests?