I expect there is a simple answer to this, but it hasn't arisen for me before:
OH is thinking of joining the electronic revolution and getting a laptop or tablet. Will we have to have a separate internet provider/account, or can he have an address linked to my desktop? I'm with btinternet but also have a gmail account.
He can just connect to the router like you do. If you are the internet account holder you'll have to set up an email account for him or he can go to gmx.co.uk (or similar) and set up his owm.
It would be best to use the broadband already supplied to your house by BT.
if your OH has another supplier of broadband his supplier will still have to use the BT lines coming to your house so it could cause confusion especially if you have future problems with broadband & suppliers argue about who is at fault.
Your OH can choose whichever email address he wishes to use ( I have 4 different email addresses)
He does not have to have an email address linked to your desktop.
As long as he get get on the internet anywhere (not even in your home but maybe even a library) he can create an email address on gmail or outlook.com or a host of other "free" email systems.
Nowadays you often need an email address to logon to a laptop or tablet.
If he is going to get a tablet then if it is an Android tablet a gmail address would be best. If he is going to get an ipad an Apple email address would be best.
If he is going to get a Windows laptop then an outlook.com email address would be best.