Really had enough now of bloody emaiks

I had the same issues. Ended up telling Gmail to immediately archive all rspb mail on arrival.

Go into <settings>  on top right of page

Select  e-mails

and deselect the box where it says    receive  e-mails 

Thank you. I have emptied G-Mail again and deselected in settings.

kathybn said:

Thank you. I have emptied G-Mail again and deselected in settings.

They might not stop immediately but they will stop. 

I remember the same problem which Tiger kindly helped me with the same advice :)