Sounds like a call to Trading Standards is required - they might be interested in hearing about this company is others locally are having trouble.
Its a pity you've paid for the whole thing - that was the mistake, but I appreciate that doesn't help you now (but it might help others reading). The rule of the game is that you don't pay all until the job is completed properly and that includes the work being signed off by Building Control (what you loosely refer to as the 'council' above) - and then you pay promptly. Builders have businesses to run.
The plumbing problem sounds like a design fault in the way the pipes have been laid/routed.