I’m having exactly the same problem. The supplied cable is about 2 ft too short. It’s impossible to fit a 13 amp socket where the router is situated, due to the way the house is.
Do BT really not supply an alternative psu with a longer lead? Surely this is not a big ask?
I haven't found a longer lead yet but I did find size changer adaptors for the Dc input socket on the SmartHub and HomeHub. They're called a "Plug Size Adaptor for BT Home Hub" if you want to look them up. These can then be used with a third party 12V wall supply and 5.5 x 2.1mm extension leads. It would be worth asking them if they also sell extension leads that plug in directly between the BT power supplly and the Hub.
@chrisjp wonder if it was a decision to make sure it was impossible to plug the incorrect PSU in to avoid unnecessary damage resulting in support calls and additional costs. IE if you literally cannot plug the wrong PSU in then tech support just wont get calls about that, money wont be spent replacing devices that have been damaged where its impossible to tell if the user did indeed over power it etc. You can observe this behaviour by many vendors in efforts to reduce the chances of things going wrong, the extreme example being Apple where you can pretty much only do things the way they let you do them.
Ive seen some people moan that its just a way to make money but I very much doubt that BT are thinking about making money off replacing PSU's.
OR.....it was a complete manufacturing oversight because they just didnt even specify to the manufacturers what they expected from that part.
Is it only the SH2 that has this DC jack type?
No, the HH5 type A was the same plug. The type B was more standard, a 2.5mm plug.