Sorry to hear about your 'run in' with an ambulance.
I've only just joined the Subaru club, but until Jan 2013 I was a Paramedic Manager at a local ambulance station in Derbyshire, which is also part of the East Midlands Ambulance Service area, which covers Northamptonshire.
In my opinion, if the crew were on a 999 call, they should firstly have had blue lights on, and most certainly the audible warning switched on.
If you're saying they hadn't either lights or siren on, then I would assume they weren't on a 999 emergency, so from what you said, it appears the driver was driving without due care and attention.
Obviously I don't know the full facts of what happened,but it my be worth reporting to the Police, if you managed to get the registration of the ambulance,(and I'm assuming it was a 999 ambulance-yellow and green 'battenburgh squares' on the sides of the ambulance body??) , and not one of the plainer liveried ambulances which just transport people to local hospitals for treatment, usually referred to as 'Patient Care Transport' ambulance.
I would give the main EMAS HQ a call in Nottingham, Horizon Place,Mellors Way,Nottingham, i'm not sure of the post code though, and explain why you have a complaint.
If the ambulance is one from EMAS, and you have the day, time of day and a reg of the ambulance,the service might be able to track the crew involved.
I know it doesn't help with the damage to your car, but if all is appears as you say,the driver should get a bo*****ing, or they would have done from me if I had been asked to investigate the same issue.
You never know, you might get some compensation, sorry I can't advise any further.
And for clarity, and having been on the ambulance service for 22 years, not everyone is a s**t drivers, just like every other driver, some aren't what we'd like them to be, but not all, believe me it isn't easy getting to a job on blue lights when someone's life is at risk in busy traffic etc.