You have acquired one of the nicest examples of a No. 4 Mk. I (T) out there. As mentioned few of these have the scope set matching the rifle and far fewer have the chest numbered to the rifle as well. Be very happy!
The No. 15 Mk. I chests were reassigned as needed, which is why it has the paper label on the metal holder on the end. The chests were used for long-term storage and for shipping. One rifle might be shipped from the UKto Germany
for example and if another No. 4 Mk. I (T) needed to be sent back to the UK for repairs etc. they would simply change the paper label and ship the other sniper set back to the UK in the chest. It was extremely rare for rifle/scope numbers to be painted directly onto the chest. From what I have seen this was usually done post-war when the set was held by a police unit or perhaps another NATO military force. Sometimes private owners have added permanent serial numbers numbers to the chest for their rifle and this has also been done on replica chests.