Yes, your currently installed SketchUps will continue to work, and in the future you could remove the 2019 license from an old machine, and activate 2019 on a new machine.
The computers that you can use by signing in to your subscription need not be the same computers that have the classic licenses. For the discount side of things, either you would look for an email from SketchUp that talks about the migration offer, and use the link in that email, or you would sign in to sketchup.com with the email address that your Classic license is assigned to. Then the purchasing system should pick up on the fact that you are eligible for the 60% discount.
If you wanted to be sure, you could call the UK distributor, probably Elmtec, and do the migration discount deal over the phone.