Steone, if you read your policy you will probably find that the basis of the contract is that it will re-imburse medical expenses etc that are necessarily incurred and caused by accidental means, subject to some exclusions. If the insurer were to start paying bills immediately, before the claim is accepted as being valid, there may be a problem later. Do you have a better suggestion on how they operate?
The unwritten advice in any such situation is that you should act as if uninsured. Try to mitigate your losses and not incur costs that are unnecessary or you would not do so, if you were paying yourself.
It's not a perfect world, insurers don't always send out forms immediately, just as some insureds inflate and put in false claims.
But all UK insurers are answerable for poor service and decisions that are wrong - if you feel this took place make a complaint to the insurer and if you still feel aggrieved lodge a claim with the Financial Ombudsman Service. It's free!
Perhaps you might think yourself fortunate that you have these options. I've dealt with the FOS several times and they are superb - far better that the Law Society or the Property Ombudsman who, in my experience, are both biased in favour of their client (I use that word advisedly).
For a lot of other purchases you make there is no Ombudsman - try making a claim against RyanAir!