If you have rendered service, and you can prove so via your contract and the admission is their email. you can for sure go into a recovery suit.
The emails are vital as it will prove their admission regarding they were liable to pay you the money
The contract would corroborate the amount to be paid and since when it has to be paid.
You are advised to file a recovery suit against them demanding the payment, Interest and legal and litigation costs.
First step I would suggest you to do is, Send them a Demand notice, in which you can claim payment and interest or penalty of late payment. this can be sent by you or your lawyer. This will certainly rattle the company into taking an action. LEGAL NOTICE OF DEMAND would help as it will be effective and cost efficient than straight away filing a suit.
Sent the notice via registered post. I'll suggest you to consult a lawyer to draft you a legal notice.
If they still don't pay, file a recovery suit.