The MP for Oxford East said people are contacting her regarding the problem, which includes delays to letters.
Both the OX3 and OX4 postcodes in Oxford have been affected, as well as OX33, OX44 and OX49 which covers Horspath, Wheatley, Chalgrove, and Watlington.
The company previously issued a warning that there would be service delays in over 100 postcodes across the country, due to adverse weather and increased sickness absences.
Dodds observed street-worth of undelivered letters and hundreds of packages in metal trollies (Image: Oxford Mail)
Miss Dodds said: “Many residents are still contacting me about issues with Royal Mail.
“It’s right that Royal Mail bosses have now been called to parliament to answer for shortcomings in service.
“I have been pushing for improvements for many years, so this is much welcome.”
Royal Mail has been called in to face a committee of MPs who have raised concerns about “chaos” in the postal service since Christmas and suggestions that some letters are being delivered in “batches”.
The MP said there was a secret visit to the East Oxford sorting office which uncovered “heaps of undelivered mail” documented by BBC Panorama.
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She added: “I’ll keep pushing for our posties to be listened to, and local residents to get the service they deserve.”
The MP said that Royal Mail has now extended the opening times of the customer service point at the Oxford delivery office.
The sorting office is now open Tuesday to Friday, between 4pm and 6pm, in addition to the morning openings on Mondays to Fridays and Saturdays.
The last time Royal Mail met its annual target for delivering first-class post on time was in 2019-20.
The firm – whose owner International Distribution Services was bought last June for £3.6 billion by Czech billionaire Daniel Kretinsky’s EP Group – repeated its call to “urgently move forward” with reforms to the service.
Ofcom last year cleared Royal Mail to scrap second-class letter deliveries on Saturdays and change the service to every other weekday.
Royal Mail has since introduced the changes as a pilot across 35 delivery offices.
On Friday, it was announced that the price of a second-class stamp would go up by 4p to 91p and first-class stamps would increase by 10p to £1.80 from April 7.
It means the cost of a first-class stamp has now more than doubled – up 137 per cent – in the past six years after eight rises, while the cost of a second-class stamp has been hiked six times.
Anne Pardoe, head of policy at Citizens Advice, said: “Higher prices must come with higher standards – increases should be tied to Royal Mail’s performance on the doorstep.”