This is kind of important, because the rules seem like they can work either way.

There are two monsters on London, a Dark Young and a Warlock in this example. On my encounter phase, do I try to beat one, then wait for my next encounter phase to kill the other, or do I try to defeat one, then try to defeat the other, all in one encounter phase?

During the Encounter Phase, an investigator on a space containing one or more Monsters must encounter each Monster on his space, one at a time, in the order of his choice.

During the Encounter Phase, if an investigator is on a space containing one or more Monsters, he mustresolve a single Combat Encounter against each Monster on that space, one at a time, in the order of his choice.

So, you have to try to beat each one in one Encounter Phase but in seperate Combat Encounters. (You can have multiple Combat Encounters in a single Encounter Phase.)

Also if you do defeat them all then you can have another encounter of your choice.

Yeah, book also says you only have one encounter per combat phase, so the wording was a bit weird. If each monster is a combat Encounter, and you normally only get one encounter per Encounter phase, then that would mean one at a time, but I don't think that's supposed to be the intent of the rules; I think your interpretation is the correct one.