I have found one setting that can make this happen in IE. If you go to the tools menu then select the following options you will reach a checkbox for "Ignore font sizes specified in web pages":
Tools -> Internet Options -> Accessibility -> Ignore font sizes specified in web pages
This basically tells the browser to ignore my font size choices, which is why fonts would overflow their containers. I've now made the containers variable size, so the overlap problem should be gone. But if you aren't using standard fonts the containers themselves might be arranged in a strange way. Not ideal, but better than overlapping text I think.
BTW, the checkbox above is an accessibility feature for people who would like to read larger fonts. It was more useful in the earlier days of the web when web pages were mostly text. These days I think people rather make the whole page bigger using the zoom function (see the bottom right of the window where you can select 125%, 150% etc.) or by using a lower resolution in Windows.
Lisa, Louise, will you please let me know whether this setting was selected in your browsers?