I actually work for the Royal Mail, albeit at a mail centre (huge sorting depot) and not as a mail carrier. No one particularly wants to strike but it's one of those deals where the workforce feels it has no other choice.
The best case scenario is that it'll go a week or two, ending at the end of this month or start of November. Management and the union have already been holding extensive talks for the last few weeks. Hopefully, both sides already have an idea of what kind of deal is possible and a national strike will be like a splash of cold water, bringing people to their senses.
Worse case? Deep into November and onto December. Neither side wants this. At a certain point, with a backlog built up by the strike, there's only so much the system can process. Plus, a lot of big parcel shippers like Amazon have already or are seriously thinking of canceling their contracts with us. If nothing else, you aren't going to get a lot of money trying to sell a burnt-out shell.
So yeah, I don't think Christmas will be ruined. It's the MAD scenario for both sides. Still, I'd mail your stuff as early as possible this year.