Sorry to hear that.
Unfortunately, you won't be allowed back into the country without a BRP, so you should not attempt to travel until you have your replacement BRP.
The reason you cannot see any appointments on the UKVCAS website is because you have to wait for UKVI to contact you by email to let you know when you can book an appointment... or if you are eligible to forego biometrics (they will reuse your previous biometrics) and instead use their new IDV (Identity Verification) app to submit an updated photo instead.
People are being contacted in application date order to book appointments/use the app so that they don't have thousands and thousands of people all trying to book appointments at the same time.
See here for more info:
https://www.ukvcas.co.uk/flash-message-detail?flashmessageId=74833From that page:
Booking an appointment with UKVCAS
If UKVCAS received your application between 12 - 18 September 2020 you will receive an email by 23 September, inviting you to either book a UKVCAS appointment or to download and use the IDV app.
If UKVCAS received your application on or after 18 September 2020, please continue to check this page for updates. We will refresh this page over the next few days to let you know when you can book a UKVCAS appointment or use the IDV app so watch this space!
Normally, you would be able to expedite the application by paying £800 for the Super Priority Service to get a decision within 24 hours of the biometrics appointment. However, the Super Priority Service is not currently available due to Covid (I believe you would have been offered the option when you submitted the application for a replacement, if it was available)... so unfortunately, you will just have to wait.