If you don't know already, some ISA's allow withdrawn funds to be replaced in same tax year - so if you have one of those, that the one to withdraw from and hopefully EST payment can then be used to repay the funds.
I have read that EST cannot be used on a car already received, so timing may prevent obtaining an EST payment.
Per the EST website. “ with exception of an initial deposit, applicants must not have made any other payments towards the purchase of the vehicle before receiving a loan offer.....”
So long as the loan offer has been made I doubt there will be an issue paying for the car before they process the payment