A normal vehicle alternator is designed to supply the vehicle electrical equipment which runs quite well at around 12 to 13.5 volts, and to replace enough charge in the battery to start the engine the next time. That amount of energy used to start the engine is about 300Amp-SECONDS, an absolutely piddling amount that can be replaced by a standard alternator in little more than a minute. Since the alternator is nothing more than a very crude taper charger with a set maximum voltage, the problem is not to get enough charge in the battery, but to stop it overcharging on a long drive. They do that by limiting the voltage to a compromise value well below the 14.4 volts that needs to be applied to a normal deep cycle battery to ensure a full charge. It doesn't matter for the starting battery, but for a deep cycle house battery - or leisure battery as you call it -- it means that under the normal cycle of hammering hell out of the battery overnight and then driving for a couple of hours to the next wild camping spot - or even worse, idling the engine for 20 minutes -- the house battery is chronically UNDERCHARGED and may rarely get beyond 70% charge even after several hours of driving. Note that the charging voltage you read on a meter is no indication of how full the battery is. Only the resting voltage gives any sensible indication. This constant undercharging guarantees a short battery life as well.
Since a battery shouldn't be regularly discharged below 50% or below 40% for AGM batteries, this means your effective safe usable capacity is 70%-50% = 20% and for a 100AH battery represents only 20AH. A big TV and a fridge drawing 3 amps and the battery is suffering by the time "The Bill" is finished.
Solar - of sufficient size - overcomes this problem because the 3-stage solar regulator can take the battery to 100% capacity if not every day, at least occasionally. Another way is to use a car alternator with a "smart" regulator that will also fully charge the house battery, or there are other systems that take the engine battery supply and invert/convert it to a higher DC voltage that makes it a three stage charger as well.
Here in Australia where caravanning is very popular, but solar is rare - and even in motorhomes without adequate solar, another way to properly charge the house battery while on the move is to use the 12VDC-240VAC inverter that many have in their van and the 3-stage mains battery charger that most also have. Get the 12V supply for the inverter from the engine system, feed the 240V to the charger, and charge the house battery from the charger. Over the full charge cycle, this is a more rapid charge than direct from the alternator AND charges the battery fully AND uses only the equipment already installed in many MHs.