The 12V leisure battery is likely to provide a MUCH more stable, spike free 12v than any of the 240 to 12v in line boxes supplied with the TV.
If the TV has a 12V DC input socket simply connect it (via a small fuse in the 'live' lead only) to the battery and bob is your fairly close male relative!
If it's a mains adaptor then you can only use it via the 3 pin mains socket so if you are not connected to electric hook up then you won't be able use it anyway. You will then have to use a compatible 12 volt TV lead which plugs into the appropriate 12 volt TV input socket and caravan 12 volt power socket.
We have always used our TV via the 12V supply when away in the van. Never had any problems and we don't even take the mains adpater away with us any more.
Just find a 12 volt lead with a plug that matches your TV, check the polarity is correct and plug it in. Ignore the doom mongers and enjoy...
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