The reason it does that is so that you don't think there is a network issue or a fault and try and report it as such to BT so in answer to your question... no.
If you use a different router, than you will get a page not found message, which you may prefer.
For example the TP-Link TD-W9970 blocks Internet access using a firewall which can be programmed to a schedule in 30 minute time blocks.
You can make this blocking selective to certain websites if you wish. Its 100% configurable.
You can block certain game sites if needed.