legal advice

Lets say someone worked for an employer for a period of five months split into three months prior to Christmas 2017 and from March 2018 until May 2018 and was paid no problem before Xmas and then agreed for the last two months of payment on completion in May. Work was done and finished to satisfactory standard but wasn't paid on completion. They were paid a sum three months later and then a smaller sum a further three months later totaling half of what was owed. Since then nothing. Doesn't answer calls ,text or emails. There was no contact signed but they have full correspondence outlining works agreed price and whatnot.
Would they have a case to bring against them ?