I think that Moggie's problem relates to the fact that inserting the headphone plug into the socket on the rear of her TV mutes the internal speakers. That occurs because, when the plug is inserted, a prong insert the socket is pushed to one side, breaking the connection to the speakers.
The use of an extension lead (as suggested above) isn't going to help if Moggie still wants to get sound from the speakers on occasions, as there would still be a plug in the socket, thus muting the speakers.
Not being able to listen via BOTH the to the speakers AND through headphones simultaneously has long been a problem in households where one person has hearing difficulties, and thus needs to use headphones, while others want to listen to the sound from the speakers. However some manufacturers have responded to the problem by introducing a menu setting whereby users can choose whether or not they want to have the speakers disabled when they insert a headphone plug. If there's such a setting on Moggie's TV, she can leave her headphones plugged in and then switch between the two audio options in the TV's menu.
So it might be a good idea for Moggie to read through the user manual for her TV set, to see if there's mention of disabling the auto-mute function. (If you need help, Moggie, please provide us with the exact model number of your TV, which you should find on the rear of it).