In a grocery shop near Rochester high street in Kent, Wayne Bywood, 34, is still seething about his experience at Medway Maritime hospital two nights earlier. “I got hit on the face, chest and shoulder by a brick that came through my car window when I was driving,” he says. “I was bleeding, had skin flapping off my face and was semi-conscious. Even though I arrived at 8.20 I didn’t get seen until 11.20 and didn’t get out until 1.20 because I ended up having stitches.

“The service was slow and terrible. I didn’t get an x-ray until I moaned that my shoulder was sore and I went from the minor injuries unit to be assessed to the AE unit for my x-ray and then back again to minor injuries to be stitched.”

His mother’s similarly poor experience of the hospital meant that, after going there after the first of her three strokes, she instead went to the Darent Valley hospital in Dartford, 14 miles west, for subsequent treatment. “I would rather spend £10 or £15 on diesel going there or the William Harvey hospital in Ashford [27 miles east] and go to a hospital where staff treat you properly and talk to you nicely,” Bywood says.

Stories like his are not hard to find among the 80,886 voters in Rochester and Strood who will choose the Kent seat’s new MP in a byelection on 20 November that is widely seen as one of the most significant for many years, especially for the Conservatives.

In La Torretta cafe, next door to the campaign office of Mark Reckless, the Tory MP whose defection to Ukip triggered the poll, one coffee drinker says: “The Medway is infamous. People here say that if you get a diagnosis there, it’s best to get it double-checked.”

When shadow chancellor Ed Balls visited recently to support Labour candidate Naushabah Khan, one elderly woman told him she was scared to fall ill in case she ended up in the hospital.

The national narrative is that the Rochester byelection will be a verdict on the parties’ stances on immigration and Europe. But voters say the ex-naval hospital is also a major focus. One poll even ranked the state of the health service as their top priority, ahead of “the impact of immigration on your local community”.

After a party conference season in which health funding pledges were prominent, and with the NHS set to feature heavily in the runup to the 2015 general election, the byelection is a portent of political battles to come.

The Medway has been one of England’s worst-performing hospitals in recent years. Deeply ingrained problems resulted in it being placed into special measures in July last year; its chief executive and chairman were pushed out earlier this year.

After a July inspection, the Care Quality Commission (CQC) said its AE unit, surgery department and overall quality of care were inadequate; its medical care, maternity services, end of life care and outpatient clinics required improvement; it relied on constant “firefighting” by staff; its AE was “in a state of crisis”, with patients being “stacked”, unable to be seen; planned operations were often cancelled; and surgical patients faced delays getting back to their wards.

In the window of Reckless’s busy HQ, a former crystal healing shop, a leaflet says he is “backing Medway’s NHS” and features praise from Dr Sanjeev Juneja, a local GP, for Reckless’s “dedication” in helping to save his Marlow Park surgery in Strood from closure.

Tory candidate Kelly Tolhurst’s six-point plan pledges that if elected, “with our next-door MPs, I’ll bring hospital staff and the national government together to get Medway hospital out of special measures as soon as possible. That hospital saved my life last year and the people there deserve our best efforts.” She was treated for a twisted bowel and recently told the Kent Messenger: “The staff there literally saved my life and without them I wouldn’t be here today.”

In her small office near Rochester Castle, the Labour hopeful, Khan, says: “Health is 100% the subject that comes up on the doorsteps. It’s the one issue that people of all ages relate to and have a story to tell about.”

When shadow health secretary Andy Burnham visited last week, voters detailed concerns about a range of health issues. “It’s about more than the hospital. People talked about inadequate mental health services, their real frustration at getting to see a GP – sometimes they wait more than a week for an appointment – and the fact that some GPs will only let them talk about one issue at a time, which is madness,” says Khan.

She is sceptical about Reckless’s bid to be seen as an NHS supporter, and sees his backing for Labour MP Clive Efford’s private member’s bill to prevent privatisation of health services as close to opportunism. She says: “It’s interesting he’s doing that because when, as an MP, he had the chance to stand up and say NHS privatisation was wrong, he didn’t do so, and now he’s saying he will vote to stop that privatisation. That’s frustrating. And he voted for the Tories’ top-down NHS reorganisation”. Having realised the NHS is such a big issue, the former MP is now “using it as an opportunity to gain leverage”.

Khan is running a poor third behind Reckless and Tolhurst, on just 16%. Polls show that 33% of those who voted Labour in 2010 intend to back Ukip.

However, Paul Francis, political editor of the Kent Messenger Group, believes that is down to Ukip’s stance on immigration, not the NHS.

But given Labour’s plans for the NHS, including a £2.5bn-a-year fund to hire more staff and the fact that health is usually the party’s strongest suit, he is puzzled why it has not made much more of the health service in the campaign.

“I’m surprised by that. Ed Miliband’s keynote speech when he came down was about immigration, which he obviously felt Labour needed to clarify its message on,” Francis says. “But, apart from Andy Burnham’s visit, Labour haven’t done much on the NHS. I’m a bit puzzled why they’ve not seen it as a good opportunity to get ahead of the Conservatives and Ukip. They have missed an opportunity here, in my view”.