It was raised because it was thought that has a Supreme Court and therefore separated power from Government it ought not be using gov.uk for its website or email address. Lord Bach, at the Ministry of Justice wrote to Lord Henley after the debate clarifying the use of gov.uk noting,
I have taken this point up and there are very sound reasons why gov is a part of the address The Supreme Court needs to operate on a very secure, robust and resilient system It will need to handle sensitive information in a secure envronrnent including the provision of remote access from a range of locations. The use of the Government Secure Internet (gsi) meets those needs in the most cost effective manner. To create a secure system of similar resilience and capability would significantly increase set-up and future running costs.Reality check. It's a domain name that points to an IP address, ergo, you could a bloody .com if you wanted and still have it working from within the GSI. No need for a new system at all with extra running costs etc etc.
NOTE: I am not saying I agree with Lord Henley. More that the argument that a different TLD such as .org would require a whole new network to be built to sit beside the GSI is bollocks.