How can I filter a view by date ranges from another content type?
It's not a dropdown list, but if you don't want to write code, consider the following.

Create a view of all UK PM's in a view. Rewrite the results to output links in the format: events/start_date/end_date.

On your events view (with 'events' path). Add contextual filters catching start_date and end_date.

You could make the first view a jump menu and show it as a block above your events view. This will have the same effect as exposed filters, but will be harder to combine with actual exposed filters.