Would I get a refund for a false diagnosis on my car?

I had a squeal coming from my car and I was never confident it was correct. I got charged £70 for them to make the diagnosis it was my exhaust manifold gasket and I declined them repairing it and took it to another garage. The garage asked if I had my auxiliary belt changed recently, I said yes, and try said the steering wasn't put back properly when I had it done. This then damaged my car. Ford said they'd pay for it to be repaired as they messed up.

As for the diagnosis, should I also ask for the £70 back from that. It was a week before I got it looked at elsewhere.

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