Please help with car insurance

Intotaldisarray

Hi everyone.
My car insurance was up for renewal today, and I rang my insurer last week to quote me for renewal (Im with kwik fit)
First of all they ask for my postcode (I changed address with tem last month yet they have no record of it) so I give them my old postcode and change my address.
Next the lady tells me my new monthly debit will be £380 (I currently pay £120). When told that I'll get quotes from else where she passes me on to someone else to get discount.
This new lady tells me because I've changed my address mid-agreement charges apply (£237)
Fine, I say. So why has my insurance jumped by £160 a month?
In July last year, I had an accident in a car park, where me and another lady reversed into each other. We both deny fault, I did not claim as I only had a cracked taillight and minor rear bumper damage. She claimed.
The lady at kwik fit tells me that the other party's insurer is still dealing with this, and hence my premiums have risen, but she can discount my payments to £270 a month. Whilst on the phone to her it appears other insurers are quoting me the same so I stuck with the nice lady.
Now, how do I go about speeding up this claim? Can I reduce my payments once it's over and done with, or do I have to wait until next year?
FYI, I've had my car for a year, been with kwik fit for a year, did have 2 years no claims bonus (assume this has gone).
Help would be appreciated
Thanks

Faith177

All you can do really is contact the claims people see what is happening with the claim and where it is at.

From there they should be able to advise you of what they need from you to help get it sorted.

Sounds like liability is still an issue on this one tbf. If you are both denying it it might go 50/50 so it will still be classed as a fault claim

InsideInsurance

If you stay with the same insurer/ broker then it should automatically correct itself if liability is settled in your favour. Obviously if you switch providers it can be more challenging.

There is rarely much that can be done to speed things up in claims short of deciding to admit blame.