We have made a claim against the main contractor , they have refuted this and we asked for them to agree to arbitration giving seven days for their response. They have not replied - what should we do next?
Assuming you have arbitration in your contract then you issue a notice of arbitration inviting them to agree an arbitrator (possibly suggesting some). If still no response you go the appointing body named in your contract.
If arbitration is not specified and you were trying to agree it in any event (which you can do) then you will need to adopt an alternate route so either adjudication or court depending on the nature of the dispute and other factors.