One person in our party must travel from Archway, on the Northern line, to Gatwick. He was going to go to Victoria for the Gatwick Express, but then noticed that the tube map shows trains to Gatwick from King's Cross/St. Pancras, and he wouldn't have to switch lines. Is going to Gatwick via King's Cross a good plan?

Yes, it is. You're quite right to use this route, as heading for Victoria would add as much time as you would save by being on a faster airport train, and would cost more.

A further thought - it's a long way from the tube station to the platforms for the Gatwick train, actually in St Pancras station next door to Kings Cross. Instead, stay on the Northern line to London Bridge, where there's another connection with the same route.

Thanks owain, this is exactly what we needed to know!

I can confirm that London Bridge would be the easiest option. I go to Gatwick this way and its lots cheaper than the Gatwick Express.