Sending something signed for is generally a really bad idea to somewhere receiving bulk mail as
1/ It won't be signed for and
2/ The Postie won't even bother going through the hundreds of items to find and 'self sign' it.
Sending with free proof of posting is cheaper and just as effective.
It's probably been delivered but not logged, just delivered in a sack with the rest of that days mail.
The police are not in the habit of prosecuting for replies received a few days late anyway, they would prefer to just progress the underlying charge.
As above, you can phone and ask if they have the reply.
Arguably as you 'know' (at face value) that the reply hasn't be received you need to make immediate arrangements to get details to them (another advantage of using proof of posting instead, as you it could create no such liability).