Nope. These regions don't have a choice about whether to opt in because they are part of larger political units that have the power to make this choice for them (as long as they remain part of those political units.)

What they are doing is trying to subvert the agreement without leaving those larger political units that are signing on to the agreement. (For the London this is the UK and for Switzerland it is the European Market.)

The elected representative of the City of London, i.e., the UK's Chancellor of the Exchequer, made the agreement.