To be hacked off with employer

[ThinWomansBrain]

Offered a new job a month ago; I choose to work part time.
Initially agreed to work two days rather than three in my current role, and be flexible with notice period until they replace me, and start my new role this Monday, two days weekly.
Then asked to continue doing three days in current role, which I've agreed to - but fuming as I've just found out that my current employer hasn't bothered to respond to reference request - so the start date for my new role is up in the air, and possibly my last weekday off for the next few weeks is spent trying to resolve things.

That’s a bit rubbish yes. Is there someone you can chase it up with?

My current employer has outsourced HR consultants, so I've cc'd them on an email to the new employer & had a chat with them, so hopefully they'll get something sent out today.
I'm at the point of thinking I'd prefer it if start date is delayed as a result.
Definitely feeling less flexible about staying on beyond my notice period to help them out.

Tbh I wouldn't have agreed to a flexible end date. Their replacement is not your concern and they clearly aren't being helpful in return if they haven't even done your reference yet. I very much work on the assumption that no company will be loyal to you as a worker when push comes to shove so why should I be loyal to them.

Hope you get it sorted quickly.