Thanks for all your replies. I think I have worked out what the problem is. I received an email for me to verify the new withdrawal address but I only just saw the email and the link expired after 60 mins so I can't verify it now. Currently on the phone with them here, hopefully they will be able to sort it for me.
I can confirm that their customer service is fantastic. I had to hold maybe 15 minutes this time before I spoke to someone but they have always been very helpful and solved every issue I have had. Having said that after confirming the withdrawal address and proceeding with another withdrawal, it still hasn't shown up on the blockchain and over the years every transaction I've made always appeared immediately even though it may have taken taken a while to confirm. I will call them back if it doesn't confirm.
Good to hear your problem is on the way to being solved. CEX withdrawals can be delayed sometimes, though Kraken is quite a big name in the industry so I'm sure your <0.001 BTC will be in your wallet soon.
While I generally advocate against the use of centralized exchanges, Kraken have been among my favorites for a long time - for their platform, service, as well as their (purported) values. Nonetheless, you should investigate using decentralized services and exchanges in the future, to avoid delays and hassle that you don't need.