When they first offered the filler role, they gave options of start dates. I selected the two that were, then, outside of my notice period expecting a call back within a couple of days.
A couple of days has turned into most of a month. Had they confirmed then, then I would have put my notice in then... and wouldn't be in this situation. Equally, under normal circumstances, they would, after a successful interview, offer a position with a five or six week start date, during which time they would carry out referencing/uniform/admin, and also giving time to work any notice. Then at your start date, you would begin training and go from there.
Not going to name either but my current employer hasn't replaced anyone who has left after they made reduncies in 2020, preferring to cover extra work with overtime, and by the same token I get stood down at least once a shift. My new employer has the opposite problem and are not being as organised as they perhaps might otherwise be, and are using the filler role as a way to mitigate staffing shortages across the company whilst working through the backlog of referencing and training. Obviously this has upset the process somewhat although I understand why they are doing it and I suspect that they haven't seen my original application which would have included my notice period.
So one might argue that I gave my current employer provisional notice two months ago and committed a month ago, albeit speculatively, to a start date next week.
I cannot satisfy both commitments. And my current employer has already, about six weeks ago, refused to review my pay based on the fact that I would be leaving, so whatever loyalty I may have had to them is rather diminished.