That is partially true, other suppliuers do have tarrifs that do not have a standing charge. But so does your current provider. Other suppliers have standing charges on their Economy 10 tarriffs (if they even support them). It appears you may have been a victim of clever marketing and partial truths.
If you don't make complete use of the the E10 meter, ask your current supplier for a tarriff change, go for E7. E7 meters are a lot more proflic and there will be many pricing and tarrif options anow open to you some will include a standing charge some won't. Which one will be better for you will dpeend soley upon your consumption of energy which you current supplier will be able to calculate an estimation for.
The answers I give you may not want to hear. The answers I give may not be easy. The answers I give will be the truth. If your prepared for this - ask away!