Booking.com took money but have no details of the booking

Heinz57Pedigree

I booked a holiday apartment in Spain through Booking.com.  I never received any confirmation email and so thought I hadn't actually completed the booking properly.  
Booking.com have now taken the money out of my bank account for the booking but are still unable to provide any confirmation details.  There is nothing showing in my Booking.com account and I've telephoned them and they can't find any details of it.  They said they will send me an email to which I can reply with the screenshots I took of the booking so they can find it.  However, I haven't received the email.

My bank says I can't dispute a payment until after 2 weeks has passed but by then the cancellation date has passed and yet I can't cancel as there's no booking showing to cancel!
I'm so frustrated and really want my money back asap.

Apart from waiting for the 2 weeks to be up is there anything else I can do?  I'm not expecting to ever receive the promised email from Booking.com as, when I initially contacted them asking for confirmation info, they responded in french with a french contact telephone number! 
I will of course respond to it if it ever does turn up but ideally I'd like a refund asap.

born_again

Have you tried contacting the apartment to see if they have a confirmed booking, & the company you were using to get to spain?

Heinz57Pedigree

born_again said:

Have you tried contacting the apartment to see if they have a confirmed booking, & the company you were using to get to spain?

I have no contact details for the company hosting the apartment as confirmation was never provided. 
I hadn't booked travel there, only reserved the apartment as there was nothing to pay for 10 days so I had time to look around and check on flight costs.

EDIT (added at 15:20pm)
I have tracked down what I think is the company and have emailed them asking if the have any info on me.  Thank you for the idea, that might help a little bit although as the money was paid to Booking.com I'm not sure how it will help getting a refund.