I can confirm that a normal VDSL modem will run quite happily of its power supply connected to a small inverter plugged into a car's cigarette lighter socket.
Deviating off topic but using
Walter's suggestion, above, will add yet another noise-generating device into the circuit! The average small inverter will be a switching based, oscillatory device which generates an approximation to a sine wave. That generated stepped square-wave (~240 V AC) is then transformed back to 12 V DC by the normal switching mode PSU.
For
Walter's Wheelbarrow, I would construct an appropriately fused distribution box which takes the ~12 V DC from the car battery (via the cigarette light socket -- until such devices become Verboten) and to which a flying lead can be connected, thus allowing the modem to be
directly powered from the car's battery.
