Hi there!
I have always had a PS when I have gone, Im sure it would have been ok to go without one, but I wouldn't chance it, I have read that there could be bridal parties having tea and that it can book up because of this....
I also had the buckingham Palace, here is what it includes:
Buckingham Palace - Our traditional tea sandwiches, scones and jam tarts complimented by fresh strawberries and cream, or a selection of freshly baked pastries, along with your choice of tea. $17.50 per guest
I loved it!
Also, I went in park attire (clean shirt and shorts, no tank top) and saw others dressed the same.
Since it is in the middle of the day, im sure they don't expect you to go back to your hotel to change before heading back to the park.
We do this on a MK day so you can just hop the monorail to and from the tea!
Hope this helped!