Okay, if your download speed is an official 20mb's with your Internet service provider in the U.K, then what is your upload speed...2mb's, because that's what will be streaming out of your slingbox in the U.K to California. When you talk about a poor picture, what is the streaming speed of the slingplayer app on your laptop in California? When you say you were getting 2000, was that in the house in England where your slingbox is located, because a local streaming speed will be different from a remote viewing speed, so basically I'm asking what upload speed are you supposed to have with your U.K internet provider and what streaming speed are you actually getting in California. The other aspect will be latency which, for me, seems to be a big factor with streaming from the U.K to the U.S west coast. I've got a 5mb upload speed connection in the U.K, but I'm only getting a 1.3mb viewing speed out of my slingcatcher in the U.S, where as within the U.K with a remote viewing connection, I'm getting a 2.6mb stream out of the slingbox. Don't ask me why, I'm still working on it, but latency and that 5000 miles distance has sucked a good chunk of my upload connection and limiting my streaming speeds. Picture is still okay though on my U.S TV. Sounds like yours is close to unwatchable.
Posting those actual numbers would be a good first start in figuring out why your slingbox picture is as bad as it is.
.....if you mean a streaming speed in the U.S of 400kbps - 800kbps then that would explain why your picture is so bad, especially with sports. Are you using the slingplayer desktop software or sling's webplayer. Some have achieved a better streaming speed by adjusting the manual settings within sling's desktop software's rather than use the default automatic settings. You won't have this option with the webplayer, but by downloading the desktop software, you can at least attempt to play around with the speeds and see if you get any improvement. There's not much else you can do on the U.S side unless your U.S or U.K Internet service provider are throttling your internet speeds.
My understanding of how the slingbox operates is that if you are streaming using the TCP protocol over long distance, then latency will be a huge factor ( press alt.shift.i on the keyboard while watching your slingbox stream if using the desktop software or ctrl on the keyboard and click the video stream if using the webplayer ). I found out that I could stream faster using what's called a SNATT stream than I could with a TCP stream, but I needed the TCP stream to make the slingcatcher work. If you can find out what type of stream you are using, you might be able to speed things up by accessing your router in the U.K and turning off port forwarding, but you'll need to be at your router in order to do so. Probably not feasable at this point.
Your last resort might be to call sling U.K and ask them to check your settings for you and see if they can tweak things on their end or recommend some changes for your router. I was told to try tweaking my MTU settings to counteract the latency I was achieving as well as check to make sure I didn't have Q.O.S activated on the router which would have limited my upload speed coming out of the U.K.
Bottom line is you might not be able to do much on the U.S side to improve speeds as latency could be the reason for why you are only getting the kind of speeds you are getting, and in order to change and test various settings, you'll need to physically be at your slingbox ( unless you have a computer in the U.K which you can remotely connect to at the slingbox location ).
Hopefully someone else from the forum or someone from sling can offer up something more helpful.
If you are still getting a poor picture quality while viewing your Slingbox away from home, the upload speed at the Slingbox location or a network restriction back in United States might be the problem.
Feel free to use the following article to retrieve some recommendations and possible causes of this issue and get it resolved.
Slingbox Answers Forum Moderation Team