I have a portable 14" TV without a jack plug. Is it straightforward to install (by soldering) a jack plug between the speaker and circuit board. I.e cutting the cable leading up to the speaker and soldering a jack plug. If this is possible will the speaker cut out the sound when headphones and plugged in?

Depend how you wire it. You can have it disconnect speaker when it is plugged in.
Or speaker could play with headphones plugged in. Switching is done in jack, not all jacks.
There is strereo and mono. Resistors are needed for the headphones.
Easiest is to salvage one from Electronics unit being thrown out.
Don't cut the wires off, may be used for new connections.