To agree with Ray, if using the machines in the UK be really sure that all the pieces of ticket have printed and that you have them all before stepping away from the machine. I often see people who have a ticket part left by somebody else, or missing part of their own. The railway companies take the position that there is a sign on each machine advising checking so it is the customer who should have checked and in the absence of those parts a new ticket needs buying.
I don't know how East Coast machines work but for the company for which I work for an Advance ticket it will spit out, one at a time, all on ticket stock, a customer id ticket with name and address, a ticket, a seat reservation ticket, a credit card receipt, and a summary receipt - all this per person so if two together all that all over again but likely combining both seat reservations onto one.
So, for sure, wait until all the churning and clanking and flashing lights finish.
That's why a lot of people prefer to print at home.