Hi Rebecca
There is a lot of well intentioned advice in the above replies. Some of it seems to be conflicting, and yet it may all be true. The problem is it might be true for the models the correspondents have but wrong for yours, as we don't know what make of model it is.
If the set was sold as being suitable to run direct from a car or caravan battery, the designers will have made it voltage tolerant.
We do know that your set is supplied with a 12Vdc 5A power supply unit (PSU). This will be a regulated PSU and will keep its output voltage tightly controlled. It is very unlikely to alter more than +/-0.5V (11.5 to 12.5V). Some electronics are particularly sensitive to voltage which is why 'regulated' PSU's are often necessary.
The caravan '12V' supply will have enough current, but its voltage may vary between 10.5 to 13.8V. This is obviously a much wider variation.
What we don't know is how your TV will respond to the wider range of voltages. It is almost certain the set will not be damaged if the voltage falls below 11.5, but it may stop working until the voltage rises.
The problem may be if the voltage goes above 12.5V we just don't know if there are any voltage sensitive devices in your set that might be damaged by the excess voltage.
Using an inverter is certainly one way, and if that is what you decide to do I suggest you look out for one that provides a true sine wave output. Most will offer a pseudo sine wave output, and these may not work with the TV sets PSU. Any inverter should be connected as close to the battery with the shorted 12V leads as possible. It is better to use a standard 13A mains extension to get the inverters output to where you want to use it.
The alternative may be the following item form Maplin.
http://www.maplin.co.uk/Module.aspx?ModuleNo=225739#Faq
This is a laptop power supply that can set to a variety of output voltages including 12V. It has a capacity of 4.5A (which should be enough for your tv) This is a DC to DC switching regulator and should provide the necessary power and supply stability for your set.