Data point: Successful Same Day Change on a BA Holidays Euro Traveller fare WAW-LHR (Booked in UK, starting from UK). Got my timings mixed up and called BA Holidays at 1am local (midnight UK) to request, and the agent initially told me I should call back in an hour (2am local, 1am UK), but then offered to hold it open on his end and make the change when the time comes, which was an unexpected offer. Worth noting I received no confirmation email of the change, however the timing had updated in MMB.