Can I ask if Billy's crate is in the same room as Alfie sleeps?
I'm just asking because I had a similar problem with Barney. 5am every morning his crying would begin. After toileting I'd put him back but he'd cry continually until we go up. I'd moved Barney's crate out of the lounge into the hall on a night so that he got used to time on his own. In the end, five months down the line, I decided to leave his crate in the lounge so he slept in the same room as my other two dogs and the problem stopped immediately. He slept right through from day one. Most of Barney's noise is when he thinks he's missing out on something, and it was in this case.
If they are already in the same room then you could try something our trainer told us. You know he's waking at 4am, so set your alarm for 3.30am so that you are waking him to take him out for a wee. When you take him out, you don't want to fuss him at all. Just give you command, I use "go do wee" when they do, praise and back into bed with the minimal of fuss. After a bit move the time you get on by 15 mins every few days. The theory is that it gets the pup into the habit of waiting for you as opposed to him waking you up.
As already suggested covering the crate can help, it did with Max when he was a pup.