If you try to make a claim, they may not even cover it considering how the damage occurred - depends on the exact policy details.
You shouldn't be doing the heating engineer any favours. If it's his fault, then he should pay. Whether he claims of his own insurance is his business and not yours. If he gets difficult and you have legal cover on your home insurance (often a separate item), you may want to explore whether they'll take up the case which may involve taking him to court. Otherwise just start with tying to claim the repair costs straight off him, and escalate from there, if necessary through the small claims court.
