You can use "Routines" (under main menu) to set Alexa to play the Big Ben Chimes on whatever hours you schedule. Select routines, click on the "+" button to add a new routine. Set the time and select the music task and type in "Big Ben Chimes" and then select the music provider (I use Amazon Music). You will have to set up a separate routine for every hour you want the chimes to play. I have mine set beginning at 5:00 a.m. and chimes set for every hour with the last at 9:00 p.m.
It will not however chime the number of the hour, you will need to set up an additional voice message task in the routine to announce the hour. You can also add a weather report to whatever hours you want to receive it and other tasks as well, even voice announcements to yourself for reminders or simply to make things more personal. For example, at my 6:00 a.m. routine, Alexa plays the Big Ben Chimes, then says, "Good morning, the time is now 6:00 a.m" and then gives me a current weather report. And at 9:00 p.m. Alexa plays the Big Ben Chimes and then announces the hour, gives me the current weather report, then the weather forecast for tomorrow, and then finally another voice announcement that says, "Good night, sweet dreams" followed by a slow, soft song that helps me relax and go to sleep.
However, you cannot reorder the tasks. The music (including the chimes) will always play last and I want my routines to start with the chimes so I have actually set Alexa to play the chimes at the minute before the hour and then voice announce the time on the hour followed by any other tasks I have included in the routine. For example, at 5:00 a.m. Alexa plays the Big Ben Chimes. Then at 5:59 Alexa plays the Big Ben Chimes and at 6:00 a.m. Alexa greets me with "Good morning. The time is 6 o'clock," and then follows with a weather report. During the hours when only the chimes play I have them set to play on the hour. During hours when I have other tasks I have set the chimes to play the minute before so that the voice announce occurs on the hour.
Hope this helps, it's the best way I have found to do this but it would be nice if Amazon would develop a program that chimes the hour.