It will be rebuilt one half at a time so that traffic can flow over the remaining half using contraflows.
About 53,000 vehicles – including 2,000 lorries and 350 coaches and buses – use the bridge every day and hundreds of trains travel daily underneath.
The works will cause travel disruption for two years.
The estimated cost of the whole scheme has since soared from £53million to £90million.
A total of 31 people or organisations responded to a consultation on the 50mph limits and on a new 30mph speed limit on parts of Old Abingdon Road, Kennington Road, and the A423 Southern bypass westbound slip road.
In both - regarding the 50mph and 30mph speed limits - 84 per cent of respondents said they were in favour of them going ahead.
Thames Valley Police and bus company the Go-Ahead Group raised no objections and the bus company welcomed the wider A423 improvement works at Kennington.
Oxfordshire County Council's cabinet member for transport management Andrew Gant is now recommended to approve the measures at a meeting on Thursday.
And Bill Cotton, corporate director, environment and place, suggested the 50mph limit on the Eastern Bypass Road is likely to become permanent in the future.
He said: "The 50mph speed limit is required to help support active travel along this section of the A423, and to align with future proposals to limit the speed along the ring road to 50mph.
"Similarly, the 30mph speed limits are required along Old Abingdon Road and Kennington Road to help support safe active travel proposals in the vicinity."
He added: "Despite the objections received believing the proposals to be unnecessary and a waste of money, officers feel that the overall objectives of the scheme - ie to help mitigate traffic congestion, improve journey times, and promote active travel in the area – justify the recommendation to proceed."
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