In next week’s Budget, new chancellor Rishi Sunak is expected to announce measures to kickstart the “levelling up” of Britain’s lop-sided economy. The Guardian visited three places which the government should be targeting – to discover the scale of the local problems, and what help is needed.

Things are looking up for Penzance. Its wonderful seawater lido has been refurbished. Maintenance and repair for the sleeper trains to Paddington have been relocated due to work on HS2, creating 70 well-paid jobs. There are ambitious plans to revamp the main shopping street, which curves elegantly from the railway station to the statue of the town’s favourite son, Humphry Davy, at the top of the hill.

But progress is slow. Penzance is the first and last town in Cornwall, a county that has the wage levels normally found in the most challenged parts of the north with the sort of house prices – inflated by the large number of holiday and retirement homes – associated with the plusher parts of the south-east. It was one of the first towns to suffer the hollowing out of retailing and it is not uncommon for residents to have five or six low-paid jobs in the peak summer season.

There are Cornish estates that rank among the highest in the league tables for multiple deprivation, and it is one of only two regions of the UK eligible for special assistance from Brussels as a result of having incomes per head less than 75% of the EU average. But the £1.4bn of investment since the turn of the century did not prevent a 56.5% vote for Leave in the 2016 referendum.

Economic hardship is not immediately obvious. As James Green, director of the Newlyn art gallery, puts it: “Poverty looks different in Cornwall than it does in an urban situation. People who come here eat in the nice restaurants, they rent the pretty cottages, they walk on the beautiful beaches and they misunderstand the challenges Cornwall faces.”

Tourism is thriving, according to Paul Ainsworth, chef patron of two restaurants in upmarket Padstow. “The biggest change I have seen since arriving here in 2005 is the staycation, people coming down here out of season. In the last year there’s been a huge surge in the number of people coming down here on an English holiday. In part that’s due to the pound’s weakness, but a lot of people are nervous, worried about terrorism and concerned about climate change.”

Yet for all the cream teas and the golden beaches beloved by the visitors, Cornwall has much in common with old industrial Britain: the loss of jobs in staple industries; the growth of low-paid precarious employment; relatively high levels of disguised joblessness caused by people leaving the workforce altogether; a struggle to prevent the young and the talented from leaving.

There remains a sizeable manufacturing base, which accounts for 10% of the Cornish economy. Eric Nichols, who runs Helston-based Spiral UK, a bespoke staircase maker, says: “The challenges are many and varied, but I would pick out logistics and connectivity. The infrastructure is better than it was but if you make stuff you have got to move it. You have got to be able to visit your customers and your customers have to be able to visit you.

It takes four and a quarter hours to get from Truro to London. It is quicker to get from London to Glasgow. I am more than 100 miles from the nearest motorway.

The Conservatives won all six Cornish seats in the 2019 general election and the government has pledged to make its new shared prosperity fund as generous as the EU money it is replacing. Yet the council is worried that the investment will be skewed towards the former Labour seats in the Midlands and the north of England that gave Boris Johnson his 80-seat majority.

Julian German, the independent councillor who leads Cornwall’s unitary authority, said: “We don’t want to be forgotten about. We face some of the systemic challenges the north faces and in terms of connectivity more so.”

The council senses there may be an inherent bias against Cornwall, because it has no big city but rather a collection of similar-sized towns strung out along the railway line that runs down the county’s spine.

Redruth is one stop of the line and on the northern edge of the town sits Krowji – Cornwall’s largest creative hub. The idea is to marry the county’s high-speed broadband – one area where it is well connected – with the students coming off the campuses at nearby Falmouth to kickstart the local economy. A new building is under construction to meet demand for space.

Glenn Caplin, chief executive of Cornwall and Isles of Scilly local enterprise partnership, says that one of the failures of the past 20 years is that there are still really challenged areas reflecting structural industrial decline: in fishing in Penzance; in hard rock mining around Camborne and Redruth, and in china clay mining in St Austell.

He wants Cornwall’s economic future to be based on high-value sectors: digital, space, geo-resources, renewable energy, agri-technology and green tourism.

This would be some transformation and for it to happen will require patience as well as cash. Penzance wants to use the money it receives from the government to create a year-round town, develop a creative sector, and encourage independent retailers back to take the place of the chains that have upped and left.

The new Premier Inn and the revamped promenade along the seafront to Newlyn are signs that change can happen. The proliferation of charity shops and a median income of £14,000 a year are signs that there is still much to do. That squares with the council leader’s thinking. “The key word in regeneration is generation,” says German. “It takes time.”

The stats

Election result Conservative MPs held all six Cornwall constituencies. Each increased their majority, by between 1.7% (Truro and Falmouth) and 8.6% (Cornwall North)

Pay Average remuneration is £19,763 (79% of the UK average, Dec 2019)*

Average house price £237,000 (UK average £233,000)**

GDP per head 68% of EU average***

Unemployment From 2.4%****(Cornwall South East) to 5% (Truro and Falmouth). Percentage of workless households: 16.5% (vs UK average 14.5%)

* Annual survey of hours and earnings, ONS

**Land registry

*** Eurostat

****2018 (latest available)