In your original unit, what is the secondary voltage of that transformer?
You can run a transformer in the reverse orientation (e.g. 220 V primary, 24 V secondary transformer will deliver approximately 220 V when 24 VAC is connected to the 24 V "secondary" winding).
Note that this is approximate, since transformers are not rated directly for voltage ratio, but for voltage delivered into rated load current.
Also, you should not apply more than the rated voltage to a given transformer winding, since that can saturate the core (even without load current).