White chocolate Creme Eggs, a ban on the computer game Fortnite and a peerage for Danny Dyer were among the suggestions in thousands of rejected petitions to parliament in 2018, revealing a unique picture of a nation’s thwarted desires.

Brexit was the issue most frequently raised, but other topics on the nation’s mind included plastic pollution, the war in Syria, dog welfare, vegan diets and bad landlords, according to examination of almost 6,000 rejected petitions. They also show a nation hungry for junk food and longer holidays, anxious about the sell-off of Wembley stadium and dismayed about everything from potholes to Snapchat’s software updates.

Parliament has invited electronic petitions from the public since 2015, which have the potential to trigger a parliamentary debate if they attract 100,000 votes. The majority are rejected for reasons ranging from the government being powerless to act, to the petition being nonsense or a joke.

The person most named in 2018’s reject pile was Theresa May followed by the Israeli prime minister, Benjamin Netanyahu, Donald Trump and the far-right agitator Tommy Robinson, who attracted attempted petitions to halt his prosecution for contempt of court. They were followed by the mayor of London, Sadiq Khan, Boris Johnson and the Conservative MP Sir Christopher Chope, who caused anger by blocking a bill to criminalise taking photographs up womens’ skirts. Chope was a bigger concern than Trump’s former adviser Steve Bannon, who was the subject of two “ban Bannon” petitions.

One petition described the computer game Fortnite as ‘a disease lurking on the internet’. Photograph: True Images/Alamy

Eighteen petitioners complained about the government’s much reviled flagship welfare reform, the pick of which was not a critique of the six-week delay in payments that forces some into homelessness, but a request to change the hold music on the universal credit helpline on the basis that it was “sound torture”.

A sardonic tone ran through many of the petitions, including a request that schoolboys be allowed to grow beards so they can practise maintaining them before they enter the world of work, a demand that Jamie Oliver stop interfering in our diets and an end to the underfilling of crisp packets.

“You expect the packet to be at least three-quarters full but no,” one petition explained. “The packet is mostly full of air. This is annoying for all of us as we pay for food, not air.”

The death of the Fall’s singer Mark E Smith prompted a proposal to rename Manchester airport after him, and the Eastenders actor Danny Dyer, who has described Brexit as “a mad riddle” and called David Cameron “a twat” for proposing the referendum, was described as “an inspiration to the British working class” deserving of a peerage.

The petition on Fortnite, a game that has spawned dance crazes and has attracted nearly 80 million monthly users worldwide, described it as “a disease lurking on the internet” that renders conversations with eight to 12-year-olds who are obsessed with it “very distressing”.

The petitions also shed a revealing light on the public’s mindset during a year that has felt tortuous for many. The verbs “stop”, “ban” and “end” were used in 733 petitions compared with “allow” and “give”, which were used 272 times.

Among a scattering of suggestions about installing speed bumps and the frequency of bin collections, other obsessions were revealed. There were 95 petitions about dogs and 35 about cats. There were repeated calls for dogs to be allowed on planes and the Eurostar.

The “cats to remain house cats” petition highlighted estimates that cats kill 275 “prey items” a year. It stretched the boundaries of possible political action and parliament’s petitions office rejected it saying: “It’s not clear what the petition is asking the UK government or parliament to do.”

Mark E Smith’s death prompted a petition to rename Manchester airport after him. Photograph: Kevin Cummins/Getty Images

A suggestion that Theresa May wear a burqa during prime minister’s questions to show solidarity with Muslim women was rejected as it was “an individual decision for the prime minister”.

A petition for the Muslim holy days of Eid al-Fitr and Eid al-Adha to become public holidays was successful, and was debated in the Commons. However it was ultimately rejected because the government said the proposals would cost the economy billions of pounds.

There were suggestions to put portraits of Harry Kane, Prince Philip, Philip Schofield, Stephen Hawking and Gareth Southgate on bank notes, make the next Doctor Who a vegan and reopen the Croydon cat killer investigation, even though the police found foxes were responsible. Mothercare should be renamed “so it’s suitable for both parents”, we should plant fruit trees in cities to feed the homeless and Oxford and Cambridge should enter only one team on University Challenge to “stop the elitism”.

Food was a regular obsession, with petitions that suggest the trials of 2018 have driven the nation to comfort eating. One read: “I strongly believe that McDonald’s breakfast should be all day as everyone would definitely buy it” and “bring back original recipe Irn-Bru, new low sugar recipe is awful!”

There were 28 petitions concerning cycling, many raising safety concerns. Photograph: Robert Stainforth/Alamy

There were 28 petitions on cycling, many raising safety concerns, including one calling for it to become illegal to drink and pedal. Another said cyclists should be banned from roads altogether because they are “a public menace … maliciously disrupting the flow of traffic”.

There was an austere tone to some. “Bring back the cane” said one, on the basis “a little bit of physical punishment never hurt anyone”. Others were difficult to categorise. “We need more room-temperature water,” said one petitioner. “I am very thirsty all my life and have to carry a water with me, because everywhere I can buy or have access to freezing cold water in coolers or in freezers.”

One petitioner wanted a three-day weekend “because who wants to work five-day a week?” and another a six-week Christmas holiday “because I have always dreamed of going around various skiing resorts in the Alps for a long period of time”.

Local concerns were often a priority. There was a petition for a second entrance to Tesco in Banbury and another said: “We want Lincolnshire county council to cut our grass. They just stopped cutting.”

In the end, however, many of the petitions boiled down to Brexit, even metaphorically. The “standardise UK crisp packet colours prior to leaving the EEU” petition complained at confusion over the interchangeable use of blue or green packaging for cheese-and-onion and salt-and-vinegar flavours.

• This article was amended on 4 January 2019. An earlier version said proposals for Eid al-Fitr and Eid al-Adha to become public holidays were rejected. To clarify: this rejection by the government followed a successful petition that prompted the issue to be debated in the Commons.