I'm about to seed a new lawn and was recommended a fertilizer for new lawn. Is it reasonable to simply pre-mix the required proportions of seed and fertiliser and spread this all in one go, or does fertiliser need to wait a while after sowing?
Yes you can, so long as the fertilizer is designed for this purpose.
A "general purpose" lawn fertilizer will probably "burn" the seedlings as they germinate, which is obviously not a good idea.
Note that any "feed and weed" fertilizer mix should never be applied to a newly seeded lawn until the grass has become established - typically a minimum of 4 weeks after germination in complete (i.e. not "4 weeks after you see the first blade of grass appear").