Thought I’d weigh in with the latest information I’ve found. I had a new heating system installed by my landlord (housing association) last year, and due to my work pattern have been using it on a standard economy 10 tariff. However now that my work pattern has changed, and winter is coming, I am in the process of switching so have been reviewing this extensively for the fast few weeks. I thought I’d post what I’ve found recently since there haven’t been any updates recently (btw I’ve found this site EXTREMELY useful, and the only one of its kind). 
I’ve found many electricity companies will indeed supply an Economy 7 tariff using a pre-existing Economy 10 meter, essentially offering you an extra 3 hours off-peak usage on a standard economy 7 tariff. To clarify, this will mean you are provided with standard economy 10 times, using the peak and off-peak charges for the standard economy 7 tariff, which generally works out much cheaper. These companies will generally not be able to install an Economy 10 meter if needed (as I do) – and will only be able to provide supply an existing meter that has already been fitted. The other companies provide a dedicated Economy 10 tariff and will also install a meter for you if required. Some companies charge for this.
To get around this, I am switching to EDF to begin with, and then plan to switch back to Scottish Power if they are able to supply their economy 7 tariff using my new (economy 10) meter. If this is not possible I will go with the next cheapest provider. EDF are the only company I’ve found that will install a new meter free of charge, and do not charge an exit fee to leave their tariff. Although some may find the ethics of this questionable, there is therefore no rule to prevent you following these steps to set yourself up with a new meter, then switching to a cheaper tariff with another provider. The meter they provide has the economy 10 charging periods built into it, so it is the meter itself which bills you correctly for each charging period. This will result in two rates (peak and off-peak) with off-peak times (for my area) set to: 12am-5am // 1pm-4pm // 8pm-10pm. Therefore, switching to another company on a standard economy 7 tariff, if allowed, will still provide you with two rates – only with 3 extra hours of off-peak usage, potentially generating great savings compared to Economy 10 tariffs (which are usually more expensive).