Sure, here are the sentences rewritten with inversion where appropriate:

1. So much uncertainty was there that the financial markets remained closed.
2. Rarely is there so much rain in March.
3. Not until your identity has been checked will you be allowed in.
4. Hardly ever has the Prime Minister made a speech as inept as this.
5. Under no circumstances are press photographers allowed to take photographs backstage.
6. Never before has so much money been spent to so little purpose.
7. Many a time have I climbed that hill as a boy.
8. By his side sat his faithful dog.