T8 36W diffused conservatory fixture from 1992 (TCP tube)

This fluorescent fixture is coupled with the Crompton Crompack in our conservatory. It uses 36W T8 which one issue is that it flickers most of the time when started up because T8 don't cope very well in cool temperatures! It currently uses a TCP tube which is 4000K triphosphor. I want to replace it with an Atlas 40W WW