Detailed Instructions: Given a travel related situation, and given a specific question about the situation, summarize the question into a title
Problem:My old passport was damaged by a cup of coffee, so I have to renew it. It will take around 2 weeks for the new passport to come. But I'm in a hurry to apply for a Tier 4 UK visa.

The old passport was snipped by the authority and would no longer be valid. But all my personal information including the number can be recognized. And the number will be noted on my new passport.

Can I make an application or even an appointment with my old passport number, and get to the visa center with my new passport?

It would be very nice of you if you can answer my question.

Solution:
Can I make a UK visa application with my OLD passport number and wait for my new passport?