An NHS England spokesperson said there were currently no known issues with bookings at the 12 coronavirus vaccination centres in and around Hull.
They added the system showed centres as full if all slots were taken and until more were released and people should wait before trying again if they wanted one closer.
It comes as a Hull resident said they were directed to a centre almost 30 miles away in North East Lincolnshire while trying to get an appointment after the age was lowered to 30.
The NHS announced the move on Wednesday, May 26, which opened the vaccine roll out to those aged 30 and 31 after it dropped to 32 on Saturday, May 22.
The NHS said in a statement the lowering to 30 meant around one million more people would be able to get a jab by booking online, with texts also set to be sent to those eligible.
GP Dr Nikki Kanini, the NHS’ national medical director for primary care, said: “Getting the vaccine is the single most important step we can take to protect ourselves, our families and our communities against coronavirus with the jabs saving thousands of lives already.
“The biggest and most successful NHS vaccination programme in history has now rolled out to everyone in their thirties.”
The Hull resident, who asked not to be named, said being given a slot in Immingham seemed “ridiculous”.
They added the site made no mention of when new Hull slots would be available and that it lacked “transparency”.
The resident said: “In Hull, a large city with hundreds of thousands of people, if you try and book a vaccine at any vaccine centre on the NHS website you are directed to the closest centre which appears to be Immingham for most postcodes.
“It seems somewhat ridiculous that a city with more than 10 vaccination centres is unable to provide vaccines for those aged 30 and over at any time and with no indication as to how long it will be until any site will be available.
“The lack of information and transparency on any government website or even from calling the NHS about it seems ridiculous. What was the point in the government opening the vaccines to this age group if they’re unable to service them or give any information on what’s happening?
“It won’t be long until the Indian variant takes a hold here and we’ll be back to square one. This is completely and utterly unacceptable.”
The NHS spokesperson said: “On occasion, appointments at centres will be booked up and naturally they won’t appear on the system until more are released.
“New slots come online frequently though, so the advice to people is to try again later if they’d rather wait for something closer to home. Anyone who isn’t sure can contact the NHS vaccination phone line on 119.”
It comes as a total of 225,272 vaccination doses were given out in Hull as of yesterday (Thursday, May 27), with 378,964 done in the East Riding according to the latest official figures.
A total of 137,499 first doses have been administered in Hull, with second jabs numbering 87,773 and uptake rates of 61.9 per cent and 39.5 per cent respectively.
The equivalent figures for the East Riding were 223,741 and 155,223 respectively, with uptake rates of 76.4 per cent and 53 per cent.