Leisure battery

When on. EHU and charger on that sounds about right

You are reading the charging voltage. (Probably a charger is supplying float voltage). Disconnect the battery  and wait several hours before testing with a multi meter. You will then see the actual battery voltage which will be almost 12.9 Volts if it is fully charged.

Is that with a volt meter or on your caravan's instalment panel?

Check this out: https://www.thebatteryshop.co.uk/car-battery-voltage-guide-34-w.asp

're your battery question; it really is quite simple: anything over 12.7v battery is fine; below that the battery is at various states of needing charging and at 12v it is pretty flat. At 10v I doubt if it would even allow a light to be turned on (ie really flat!). A battery should be kept pretty well at full charge all the time. In winter I remove mine and store it in my garage checking the reading every couple of weeks using a multi meter and putting on charge if necessary. So in summery any reading below 12.6v and I would put my battery on charge.

The normal charging voltage is around 13.8 volts, 

Here’s the complicated answer (life is rarely simple!). A lead acid battery in good condition has an unloaded voltage of 12.7 volts. After immediate charging this voltage can be higher so you need to leave it a few hours before checking.

The correct charging voltage for a sealed battery is approx. 14.3 volts. If you have a standard charger on a caravan it will normally sit at around 13.8 volts which is a compromise which will keep the battery topped up without putting excessive voltage on the nominal 12 volt caravan system. This is insufficient to properly recharge a discharged battery so you would need to take it out of the van an put it on a decent charger.

Most motorhomes and many caravans have a so-called intelligent charger like the Sargent. When on EHU the van would be on a separate “12v” supply whilst the battery can be recharged at the correct, full, voltage of up to 14.4 volts.