Bear in mind that the 12V output from the mains transformer is a REGULATED and steady 12V DC
The output from a motorhome Leisure Battery is an UNREGULATED output of nominally 12V but actually anywhere from 11.5V to 14.7V depdending on what is going on.
Using that kind of supply on a device that is likely designed to expect and accept a strict 12V supply is asking for trouble. It may not fail immediately but it is not a clever idea unless you KNOW the unit can accept that level of fluctuation (I assumed these are not cheap either? Who pays for them if they break? I guess the NHS? in which case, it doesn't matter if they break as you can just get a new one, can't you? And saved the cost of an Inverter as well? Win-win

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