Whenever you engage a good letting agent it will ask you to sign its terms and conditions, so it sounds like your contract doesn't cover dealing with the tenant not paying rent. The money you pay will have been to deal with general problems and making sure the property is legally let.
Action needs to be taken immediately - if rent hasn't been paid since October, action should have been taken back in November.
If you think you have a case against the agency, which will depend on your terms and conditions, write to the agency and explain your reasons for complaining. If you aren't happy with its response, you could escalate the complaint to the Property Ombudsman.
I would contact the tenant yourself to find out why they are not paying the rent. It may be because they have asked the agent for maintenance work that hasn't been done. Make sure you keep copies of every written communication or write it down if verbal with both the agent and tenant.
If you don't get any joy with the tenant or via your insurance company, evicting a tenant can take time and much depends on the contract you have with them. The good news is that as soon as legal proceedings are started, most tenants tend to leave, so hopefully you won't have to worry about court and bailiffs.