Most of the rule-times make sense, but why 138 minutes?
There are two distinct routes across the North Atlantic, one using Iceland’s Keflavik airport as a key alternate, and another, more southerly route using Lajes in the Azores. West of these islands, there’s a small, triangular area which is not within 120 minutes of any suitable airport. A 138 minute rule-time (120 minutes plus 15%) removes this last “no-go” area over the North Atlantic, and the UK’s CAA approved operation under this enhanced rule for several carriers. (180 minute ETOPS is significantly more difficult, and with no reason for it over the Atlantic, many carriers neither need nor want the added expense.