Same problem, always briefly at 5pm(GMT) and then again massively at 7pm (GMT) which lasts through until about 10-11pm.
My wife and I have the same problem, we have very different computers. A friend who lives in the same town (in the South West of England) also has the same problem, as do 4 others I know that play the game all around England. Same times.
The big improvement last weekend that was due to happen seems to have done very little if indeed anything, as the problem is getting slowly worse.
Due to this issue I have been killed many times (I'm glad of the no death penalty atm) assigned skill points incorrectly and I have lost a rare item in the post. All this because the the same problem.
I should note that this problem isn't restricted to those times, but those are the worst.
I have made in game tickets (which of course, all vanished because the problem was in effect at the time) I made tickets a week or more ago on the website - no response. An e-mail to tech support has been sent, only an automated reply so far.
I (and many others) reported this issue during the beta test too.
I even contacted my ISP(the line is amazing, no problems found) and re-installed windows to see if that helped, it didn't.
I've added this post to show that the others posting here are not the only ones that have the problem, and in the desperate hope that someone who can fix this will read it.