Just tried to watch the replay video of the England v Tonga game but on my BT Youview box it was constantly stuttering.
In the end switched to watching the browser stream on my laptop second-screened to my TV over an HDMI connection and it played perfectly.
Suggests to me there is a bottleneck somewhere between the Prime Video servers and the BT Youview servers and it couldn't handle the demand. An earlier playing of the extended highlights of the Italy v NZ game played fine.
I am having the same problem with today's Scotland Vs Australia game. Stream works fine through my Chromecast, unwatchable stuttering on the BT box.
I watched the Wales game earlier this morning on the Youview box and it was fine. Tried the England game again and this time it was fine. Seems to confirm that it is a time related server-load problem somewhere upstream but *not* at Prime Video Central as I watched the Scotland game live(ish) on my laptop just fine.