Graham
To have a successful TV/inverter system I have found the following........
The TV should be an LCD that only has a mains input that is stepped down to a low power DC supply, often 12 volts.
When this type is powered by an inverter, the DC supply is uniform and free from interference, unlike a direct supply from the caravan battery.
The inverter should be a modified sine wave type, no more than 200watt output or you will have to cope with a cooling fan, and worry about it over heating.
The inverter needs direct fused connections to the caravan battery, using as short a lead as possible. This can be via a cirgarette type socket. A long cable or the caravan existing sockets impose a restricted 12volt supply to the inverter and poorer performance.
My system uses a Mikomi 15" colour LCD and a Paice digibox on Sky Freesat. My 150watt inverter, set up as above, powers both with no touble. The setup gives perfect TV and radio reception and has been tested as far south as Toulouse,France using a standard Sky 55cm dish.