"I must to England" in Hamlet: What does "must" mean without an infinitive?

What did "must" mean when used as a non-modal verb (sorry, I don't know the technical term) in Early Modern English? For example:

I must to England; you know that?

(Hamlet, Act III, Scene IV)

Solution 1:

It’s still acting as a modal verb here; this is an ellipsis for

I must [go] to England.

The OED glosses this usage, under the main sense of “expressing necessity,” as “(b) With verb of motion understood. Now arch.”.

(Must does also have some non-modal usages: “to become mouldy, musty, or mildewed”; “to dress or dust with hair-powder”; “of a male elephant, etc.: to come into a state of musth”. But I suspect none of these is what you, or Hamlet, meant.)

Edit: an earlier version of this answer described this instead as the OED’s “(c) with implied infinitive taken from the context,” which arguably fits, but I think the more specific (b) is probably more apposite here.