Footman James breakdown recovery issue

It's a shame that one of my first few posts is going to be a rant about what I thought was a reputable insurance broker.
We were heading back to Manchester from Staffordshire in the early hours of Sunday morning and the accelerator started to mishebave. It felt as though the throttle return spring wasn't doing its job. I called the Footman James breakdown recovery number and was told that there was no record of our policy on their system and they thought it was a little strange as they believed the information was sent a matter of days after the policy commences. We took the policy out on the 8th June so I was more than a little miffed that the information had not been passed on to them. They did however offer to come out regardless but could not confirm that the costs would be covered by our policy. Now I'm sure I'm not in a minority here of people who do not travel with a full compliment of insurance documents so I was unable to confirm whether or not we actually had the cover and was not prepared to take the risk and be left footing the bill. Luckily I am mechanically minded so when I had a look under the bonnet I found that that throttle arm return spring had snapped so I was able to cobble together a temporary repair and drive home. On calling Footman James today and being passed to varioius departments, plus receiving various calls from different people, I was told that the best they could do was to offer me an apology. They told me that the information is only passed to the breakdown recovery firm at the end of the month following the month during which the policy commenced. Also, it appears that they would rather lose a customer through a policy cancellation than offer a small refund. All it would take would be a small percentage of whatever part of the premium is for the breakdown recovery.
Anyway, I am now looking for new quotes despite being told that I would still have to pay a third of the premium plus an admin fee even though I have only been insured since 8th of June!!! Am I being unreasonable or does anyone else think this is a bit off?

the refund policy of FJ is the same as most people

as with all insurance you get a 14 day cooling of period, in which you on have to pay for the 14 days that you had the policy open, so you could try that one

as for the breakdown that does suck, and not sure what to say about that

i alway carry photocopy documents in my cars, for peice of mind and also the shut the coppers up when they have pulled me in the past