Starting June 22, new biometric appointment bookings will be possible! It will be available in the order you submitted your application to UKVCAS.
Here's exactly what it says on the site:
Updated: 19 June 2020
Making progress
We’re doing everything we can to offer as many appointments to as many people as possible. From Monday 22nd June 2020 onwards, we’ll be releasing more appointments, adding new service points and opening the booking system to more customers in phases based on registration dates.
Taking a phased and organised approach
In order to be fair to everyone, we are now opening up the booking system in date order starting with people who registered with UKVCAS before the 27th March but did not have an appointment. We are working from the earliest to the most recent registrations as we think this is the fairest and best approach to take. If you are one of these customers, you will have an email from us on the 21st or 22nd of June asking you to book an appointment. The email will have full instructions about next actions.