Pubs, bars and hotels have reported a “Burnham bounce” in optimism as a result of the prime minister’s overtures to the sector, polling suggests, but they warn that the goodwill could evaporate without further tax relief.

Andy Burnham has positioned himself as a staunch ally of the UK’s hospitality industry both before and since his arrival at No 10, last month announcing a discount on business rates for pubs, clubs and live music venues.

The result, according to a survey by multiple trade bodies, is that 37% of businesses in the sector now feel that his government will benefit hospitality and brewing, which are collectively worth about £100bn to the economy.

The degree of optimism is more than double the 18% recorded before the policy on business rates was announced, an increase described by the trade bodies as a “Burnham bounce”.

The government has signalled further reform of business rates to ease pressure on the sector. But with the details still uncertain, some venue owners have warned that the steps taken so far have done very little to reduce their groaning pile of rising costs.

The survey findings, shared with the Guardian, also show that the industry believes the tax burden – in particular VAT – is continuing to hold back the sector.

Three-quarters of respondents pointed to tax as the biggest barrier for businesses, with political instability (37%) cited as the second biggest.

The survey was compiled by the British Beer & Pubs Association, UK Hospitality, the British Institute of Innkeeping, and Hospitality Ulster.

“The new prime minister’s action to back hospitality has clearly driven a boost in the sector’s optimism, yet significant challenges remain,” said the trade bodies in a joint statement.

“The support for pubs and live music venues on business rates was a great first step, and now we need to see wider support and conditions to allow the entire hospitality sector to grow and create jobs.

“Our tax burden – amongst the highest in the economy – along with new regulatory costs is overwhelming us and the real victims are high streets, jobs, and communities. A lower rate of VAT, wider permanent business rates reform and changes to employer NICs [national insurance contributions] would help deliver the prime minister’s bold ambitions for every postcode.”

More than 330,000 people have signed a petition calling on the government to cut VAT on hospitality from 20% to 10%, a sector-specific relief that would bring the sales tax on the sector in line with that in many European countries.

However, critics have said this would be an inefficient way to spur growth and would cost more than £10bn, much of which would benefit large, profitable multinational chains.

A government spokesperson said: “The chancellor prioritised support for the hospitality industry in his first week in the job when he cut business rates by 20% for pubs, social clubs and live music venues – saving thousands of locals over £1,000 a year. This is on top of providing a tax break on poured pints and capping corporation tax.”