We spoke to SMBC about this during our Iron Bridge meeting earlier this week. They didn't overwhelm us with detail but the gist of it is that the investigations into what is missing and available has gone pretty well - a significant amount of the original stone has been identified and set out in the park. (I'll add some photos for those of you who have not seen them later.)
The money for the rebuilt / restoration is in next year's budget, so the work to rebuild cannot start until the new financial year. The officers we spoke to could not advise how soon after this the work would start, but hopefully it will not be too long.