No phone will allow you to connect to any network other than that of the sim in the phone. All that matters is that you try to connect to another network (that's not served by o2). By attempting the connection, you disconnect from giffgaff, forcing it to set up a new connection when you later ask the phone to connect to giffgaff.
However, if you're saying that no other connections are offered (other than possibly o2 or other networks carried by o2) -- then that probably means you're in an area where none of the other three networks have service. In that case, try again when you next go somewhere.
Unless you're in a very remote area, you should be able to find another place where at least one of the other networks has some coverage.