The plans for the stretch of road between Oswestry and Montford Bridge are set to be discussed with the government in the coming months.
Councillor Steve Davenport, Shropshire Council cabinet member for highways, said he was looking to set up a meeting with transport minister Grant Shapps “as soon as possible”.
Councillor Davenport said he is confident the dualling would remain high on the agenda under PM Johnson.
He said: “I managed to have a very good working relationship with the last cabinet, which resulted in the North West Relief Road in Shrewsbury getting funding and they were also very keen on the dualling plans.
“Now I will continue to work with North Shropshire MP Owen Paterson and the Welsh Government to get this area around Oswestry dualled.
“I will be aiming to schedule a meeting with the new transport minister very soon as I had a good relationship with his predecessor to ensure that this remains high on the list of priorities.
“I remain very confident that this is a project that will get the funding and will prove a vital gateway to Wales from the West Midlands.”
Councillor Davenport said use of the Mile End roundabout was also up significantly.
“The average rate of increase in traffic on the roads is about five per cent annually. At Mile End it is currently 15 per cent.
“These are very big numbers and we need the dualling in place to deal with it.
“I am confident I can get the right people from Boris’s cabinet and highways department around the table and continue to push it.”
He added: “I am so pleased as well that the Welsh Government is backing this scheme.
“Their support means a lot to us and to know we can call on them for support is fantastic.”
It is one of the only sections of the A5, which runs between London and Holyhead, to be single carriageway.
Figures released last year showed that since 1991, there have been more than 1,785 casualties on the A5 north of Shrewsbury up to the Welsh border at Chirk.
At the last count, 1,407 of these were slight, 320 were serious and 58 were fatal.