The Elland-based firm said pre-tax profits jumped 21 per cent to £63m in the year to December 31 despite the challenging conditions.
CEO Martyn Coffey said: "Last year was probably one of the most challenging. The Beast from the East had a big impact, but we still came up with very good numbers.
"New build is strong, infrastructure is growing and cities are becoming more pedestrianised. Leeds has done it and London has done it."
Talking about the economic and Brexit uncertainty, he said 95 per cent of the group's sales are in the UK and 89 per cent of the its materials come from the UK.
"Brexit is causing uncertainty, but we are not seeing the impact," he said.
"However, we cannot continue with this uncertainty."
The group reported strong demand for its anti-terrorist street furniture. Recent events have raised awareness of the vital role that barriers and other street furniture can play in preventing terrorist attacks and this is a rapidly growing area for the firm.
Marshalls has focused on terrorist prevention furniture that blends into the background, such as seaters or planters, rather than barriers. The group’s street furniture has steel rods enforced with concrete.
“If a vehicle hits it, it’s like hitting a brick wall,” said Mr Coffey.
“Sports stadiums are investing in this areas and we think it will carry on growing. We are selling to the Middle East, North America, mainland Europe and the UK."
Revenue rose 14 per cent to £491m in 2018 and the final dividend was raised by 18 per cent to 8p per share. There is also a supplementary dividend of 4p per share, reflecting better than expected year end debt levels.
Marshalls reported strong trading in the first two months of 2019 with sales rising 16 per cent, boosted by an 8 per cent rise from its £17m acquisition of concrete brick manufacturer Edenhall at the end of last year.
Mr Coffey said the acquisition of Edenhall represents a significant step towards achieving further growth in the New Build Housing market.
He explained that most bricks are made of clay and concrete provides a good alternative that is cost-effective at a time when the UK is suffering from a shortage of clay bricks and is having to import them.
The group is looking at more acquisitions and has a list of companies that it is interested in buying.
"This has been another year of continued growth and the business is doing well," said Mr Coffey.
"We are cautious about the political uncertainty, but the year has been a good one for Marshalls."
Analyst Graeme Kyle at Shore Capital said: "Marshalls has again demonstrated it is a class act.
"Recently acquired businesses, CPM and Edenhall, are both performing ahead of management’s initial expectations and current trading across the group is strong.
Analyst Clyde Lewis at Peel Hunt added: "Marshalls' 2018 results saw pre-tax profits come in slightly ahead of expectations.
"Market conditions haven’t been easy (weather and underlying), but the group has continued to make organic progress, helped by organic investment.
"2019 will benefit from the recent Edenhall acquisition as well as better results from CPM and recent capital expenditure. We upgrade our pre-tax profit forecasts by £1m for both 2019 and 2020 and move our target price to 530p."
Mr Coffey said the group is increasing its expenditure on research and development with a focus on innovation, new product development and service to drive sales growth.
Marshalls said its capital investment programme includes the new £3.5m static crushing plant at Howley Park near Leeds, which is capable of crushing seven different products at a time, reducing operating costs and improving efficiency.