It is incredibly nice when your ten plus year long dream finally happens. There were too many excuses, inconveniences, bad timings, budget limitations and what not for too long, but when you get a deal at work to be away for a month without consequences, there is no way to say no.
November is a good month. For flying to South America, particularly. They say you should go in December instead (warmer), in January (peak summer), February (the skiing month for me), March (tourists gone) but November works, too. It's late spring/early summer then, the camp sites and hotels start to fill up, it's not possible to get last minute bus tickets any more and there are plenty of people around who have just done what you're about to do, sharing tips and advice, and a lot more people attempting to follow your route afterwards.
The flights are reasonable (£700 return for London-Punta Arenas). The non-existent time difference of being three hours behind from the meridian means no jet lag. You get to speak Spanish, which already is a major bonus. Luck permitting, the Atlantic flight can happen on a Dreamliner, with decent sleep cycle and leg room. Santiago to Punta Arenas flight lands at dawn and catching a bus straight away means you are in Puerto Natales by breakfast. It's all quite convenient for compressing as much long haul travel into as short time frame as possible.
Going to Patagonia has no downsides.