In refusing to lift the 1% public sector pay cap, chancellor Philip Hammond is condemning “just managing” civil servants to wage cuts of up to 20%, the Public and Commercial Services union has said in response to the budget.

The union wrote to the Treasury this week to call for the cap to be lifted and highlight new research that shows from 2010 to 2016 average civil service pay fell by between 8 and 9% in real terms.

The study, which uses Office for National Statistics data and was published this week, also found maintaining the 1% pay cap until 2020 would mean the value of pay falling by 12% when measured against consumer prices – and up to 20% if measured by the retail price index that includes housing costs.

The decline in civil service pay has been greater than in the rest of the public sector and the wider economy, according to the research carried out for the union by pay and employment expert Dr Mark Williams of the University of Surrey.

In her first speech as prime minister in July, Theresa May said: “If you’re from an ordinary working class family, life is much harder than many people at Westminster realise…If you are one of those families, if you are just managing I want to address you directly.”

PCS general secretary Mark Serwotka said: “By any definition, the government’s own workforce, who are facing a 20% cut in their pay, are ‘just managing’ and deserve the help the prime minister promised they would get.

“We will continue to fight to break the 1% pay cap and to stop Theresa May’s government condemning civil servants to three more years of wage cuts and hardship.”