I did this the other day, stayed up to 1am, phoned up and booked two F (1st class) tickets from NRT-LHR-EDI, no issues at all, took about 25 minutes.
One thing the CSR said was that when I booked the outbound, I should have called them and let them know what inbound I wanted and they would have called me at 1am to complete the process. Have you tried that?