Shower tray always fills with water and then drains OK once a plunger is used

You have a clog in your drain line probably a lot of hair in your P trap, or further down the line. Here are some videos that may help,

https://www.youtube.com/watch?v=BGDYaKPAKNI

When you get to the stupid bikini experiment... you have gone too far?

As said above: you have blocked drain. You will have to snake it. Remove strainer ( drain cover ), insert cable and go full length of the snake. Do it several times. Flush with lots of hot water.

Hope that helps

Milo