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Is there any way of forcing a site to remain in portrait mode on a mobile phone.

Thank you ...

There is no standard solution for this. This will require a third party script (if possible).
You can add custom script via the HTML object.

Perhaps one of the following urls will be of use. Note for information only all credits go to the original posters in the URLs below.
https://stackoverflow.com/questions/264 ... ve-website
https://stackoverflow.com/questions/436 ... le-website
https://code-boxx.com/lock-screen-orientation/