If the salesman is simply suggesting insuring an already broken phone and then claiming under that insurance, you'd both be guilty of 'fraud by false representation' (or 'by failing to disclose information'), under the Fraud Act 2006. The maximum penalty is 10 years imprisonment (plus a fine)
However some insurance-based services do allow you to join once an emergency has already occurred. For example, some car breakdown services (AA, RAC, etc) will provide a breakdown service to a non-member who phones them, but only by charging a hefty fee and getting the motorist to sign up for membership.
It's possible that the salesman might be offering you a similar service, where you'll get your phone repaired as if you had already got insurance cover in place, but you'd then find that you were committed to paying further insurance premiums for a certain fixed period in the future.
Chris