"manage my booking". codeshare passengers used to be able to pull up their flights on JL MMB page. But JL has "fixed" that more than a year ago already.

whether you can do it on BA system yourself is up to BA. But at the end of the day codeshare flight is like you've bought a regular BA flight. The only difference is on the day of departure, you go to JAL counter and JL staff will be responsible for bringing you from LHR to TYO.