"The first thing to determine is whether or not this issue is affecting your access to all worlds or if it is a world-specific issue. Typically you will run into this speed bump if the world you are trying to connect to is full. These messages relate to an issue when you're trying to log in to a highly populated world (though, it does seem to place you in-game for a moment, before kicking you out again). The problem however is intermittent, so if you keep trying to enter the world you'll eventually get in.
The problem can occur when trying to log in to any world, but is prevalent on busy servers, and especially those used for Dungeoneering, as Dungeoneering is more punishing on the server than other activities. W2, W34, W77, W84, W88 and W117 are particularly affected. In addition, it's best to avoid worlds that players are automatically logged into, as these tend to be fairly populated; instead, look for niche and non-themed worlds.
It is also possible that the world you're trying to connect to is offline which can happen occasionally. To check this, please refer to the Known Issues & Customer Service Notices found at the top of pages in the Support Centre. In this case, unless all the worlds are down for maintenance, then switching worlds is still a good plan." Tech help- RS Wiki