I asked about upgrading each leg of a LAX-LHR-LAX in 2006 and they told me they didn't offer paid upgrades.

Once on board and seated, however, I did see another WP+ pax negotiate a paid upgrade with the purser.

I thought I heard them agree on 100 pounds.

Purser took pax's credit card into the room under the stairs, came back about 5 minutes later, and moved him up.