I've changed my DNS settings. And all other changes that Afriman has suggested.
The slow speed at the time was across multiple ISP's but that was only for couple days.
All the testing I've today shows the problem of downloading and being unable to browse only on Afrihost accounts. I've tried both Afrigreen and my normal Afrihost business account.
I've tested on Web africa account today and was able to download and browse simultaneously.
Tried downloading a torrent now. Torrent downloading at 700kbps and I'm able to browse.
So whatever problem I seem to be having is only related to direct downloads where I can't browse and download simultaneously. So far anyway.
Not sure if this has been asked yet, but is this browsing issue present on all your browsers?