Boris Johnson will announce a range of tax cuts for businesses at the Confederation of British Industry conference, as the business group’s director general warned his plans to reduce immigration risked a skills shortage.

The prime minister will promise tax relief for the construction and research industries, plus a tax cut for small employers by raising the allowance for their national insurance bills from £3,000 to £4,000. This comes on top of a previous pledge to lower business rates to help those with premises.

Johnson will also attempt to turn around his image as a politician who prioritises leaving the EU over business concerns, after he was previously reported to have said “fuck business” in relation to worries about Brexit.

He will tell the business lobby group’s conference on Monday: “Let’s not beat around the bush, big business didn’t want Brexit. You made that clear in 2016 and this body said it louder than any other.

“But what is also clear is that what you want now – and have wanted for some time – is certainty.”

Ahead of the conference, Carolyn Fairbairn, the CBI’s director general, raised concerns about Conservative plans for a tougher immigration regime after Brexit, which would stop migrants coming to the UK unless they had jobs and could pay a health surcharge of £625 a year.

She told Sky: “When we hear talk about brightest and best, I think that is a worry. If you do want to build 200,000 houses a year, you don’t just need the architects and the designers, you need the carpenters, you need the electricians, you need the labourers. We need people to come and help us renew our economy.”

She added: “It’s not just brightest and best, it’s people at all skill levels across our economy that we need.”

Jo Swinson, the Liberal Democrat leader, will appear at the same conference to argue that her party is now the best choice for businesses because of its stance on revoking Brexit.

“The Liberal Democrats are the natural party of business,” she will say. “With the Conservatives in the pocket of Nigel Farage, and Jeremy Corbyn stuck in the 1970s, we are the only ones standing up for you.

“Because we believe that any form of Brexit, whether it’s hard or soft, blue or red, will be bad for jobs, business and our public services.

“We believe that being part of one of the most successful economic blocs in the world is the best guarantee we can have for the future success of our businesses and of our country. We believe that our best future is as members of the European Union.”

Jeremy Corbyn will also give a speech at the conference, which is likely to focus on his party’s plans for a green industrial revolution.

The Labour leader is expected to announce plans to create 320,000 “climate apprenticeships” in the party’s first term in government, paid for out of the current apprenticeship levy on companies.

He will say the apprenticeships would be available to train more engineers and technicians in renewable energy and transport, civil engineers and skilled tradespeople in sustainable construction, designers, welders and fabricators in low-carbon industries, and sustainable agriculture and forestry specialists. At the conference, Corbyn will say Labour would put in “public investment to create good, clean jobs, tackle the climate emergency and rebuild held-back towns, cities and communities”.

However, Fairbairn criticised Labour’s plans for sweeping nationalisations. She said Corbyn’s plans for utilities, broadband, the postal service and railways would “freeze investment” and called on him to work with business.

She said: “We look at the policies on the table and we have real concerns that they are going to crack the foundations of our economy. I have talked to businesses who are already sitting there thinking ‘maybe we’re next’.

“So we do say again to Labour, work with business, work out different answers to these problems. But this programme that is appearing to value none of the contribution that business makes will simply shut investment out of our country.”