Double Indemnity?

It certainly works that way with accident insurance. But I don't think it is an issue for breakdown cover, and the one you call comes and does the job. So long as you don't claim the same accommodation costs after a breakdown from both it shouldn't be an issue. A bit like when a new car has breakdown recovery included. You still have your private motoring cover which has more in the way of extras, and in flexibility with a network of agents, rather than the lesser number of dealers for the car brand cover.

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Just had a word with my daughter-in-law, a commercial lawyer, about this. She said......

1) It is not "double indemnity". You are not being indemnified. Double indemnity relates to life policies where you are indemnified to receive an increased payout for certain conditions such as unexpected or accidental death, as compared to more natural circumstances.

2) There are no laws preventing you from having more than one cover for the same thing e.g. insurance plus motoring organisation. There are laws relating to making multiple claims for the same event. These laws are in the class of fraud.

3) If you have multiple cover for the same event such as vehicle recovery, then it is your choice as to which provider you elect to make or fund a recovery. You just cannot obtain an advantage from more than one for the same event.

4) Insurance companies may sometimes have policy clauses relating to multiple cover. Doing so may void the policy. Again, it is not 'illegal' to do so, merely the risk of voiding the policy or possibly attempting to defraud.
Advice was to ask your insurer or read your policy even if it is extensive and boring.