Contractor Balfour Beatty, which is refurbishing the structure, said the work was progressing well.
The bridges old white iron lattices are back in place and the workmens hoisting crane and barge will pack up soon.
The lattices no longer support the structure as it has been successfully reinforced with 24 steel girders and three new pier supports. These transfer the weight of passing vehicles on to new foundation piles set 30m into the river bed.
The engineers will soon begin resurfacing the road in readiness for the bridge to re-open.
An exact date will be known once utility companies publish their timetables for relaying pipes and cables.
The toll bridge, which is run by a private company, is more than 100 years old and needed strengthening to cope with modern traffic flows.
It closed in October and was meant to re-open in April but this date was put back due to problems with dismantling the old structure and floods in January and February.
When the bridge re-opens, the cost of crossing on a pre-paid card will go up from 20p to 29.4p.
The 40p cash toll is not affected but the company says it will be reviewed later in the year.
Geoff Weir, secretary of the Whitchurch Bridge Company, said: Things are moving quickly now and we should be able to give a date in a week or so.
We remain confident that the bridge will re-open before the end of September.