[blam]

"How deep is the water between the Falklands and the mainland? Since ocean water levels were hundreds of feet lower maybe they walked over during an ice age"

Take a look. Here's a map of the whole earth with the oceans water reduced by about 310 feet.

[DuncanWaring]

Hmmmmm ... looks like some swimming would still be involved.

Or, during an exceptionally cold winter, it might form an ice bridge.