Janet
Hi from a newcomer to the FOC.
You shouldn't have problems getting a tyre repaired unless the puncture is close to, or in the sidewall. You can have up to two PERMANENT tyre plugs done before having to throw a tyre. AA-type roadside repairs are only temporary however, and as they tend to open up the puncture too much to fit their plugs, then you DO have to bin the tyre afterwards. No one will want to repair a tyre that is close to, or beyond legal tread-depth limit, and certainly would not be advisable to do anyway.
Nick Crisp