(Edited) I have to say this has dramatically improved over the years. I can now happily watch Wimbledon in HD on my Sony TV, using the BBC Sport app over my TalkTalk home WiFi (approx 4-8 Mbps). Sadly, the same cannot be said for the same app on my Virgin TiVo, which keeps freezing, making it a bit difficult to follow a match. You'd think the TiVo would be better as it has its own dedicated hard-wired Internet connection.
I tried to select matches through the Red button on TiVo on the first day of Wimbledon, and it was taking 5 minutes just to select a match. So I've reverted to simply switching through channels 108, 162, and 990 thru 995 to see what matches are on.
Quite frankly, I can't see the point of offering different matches through the red button on TiVo, if you cannot switch in a timely fashion.
The advantage of the BBC Sport app is that you can watch in HD. I tried the TiVo app again today and had to give up due to picture freezing. You're right, John, in that it also takes ages to actually get to the match. My Sony TV is much quicker and more reliable.