If you're unlucky enough to break down while your pets are with you, you'll still be able to receive roadside assistance. But transporting Fido and Tiddles is at the discretion of your insurer.
RAC says it'll always attend vehicles carrying pets, but will decide on a case-by-case basis whether it's safe for the pets to travel in the recovery vehicle, or your vehicle if it's being towed.
The recovery driver has discretion over whether the pet can travel in the vehicle. However, pets are usually allowed to travel with the recovery driver unless they are distressed or vicious, or the driver has allergies. Unless there's a safety risk, guide dogs will always travel with their owners.
The AA says it'll transport any animal with its owner, unless it's not possible for health and safety reasons, at the risk of the pet owner. However, it does not offer transport for livestock and horses (for obvious reasons).
If you have pets in the vehicle with you when you break down, let your insurer know when you contact it for assistance.
For more information, check page 16 of the AA's policy booklet and the RAC website.