I know you said that “normally” burglary is accompanied by forced/violent entry, Jack, but that is not the definition in law. A person is guilty of burglary “if he enters any building or part of a building as a trespasser with intent to steal,...” You can see from that wording that no forced entry or violence is required and no actual theft needs to have taken place (so long as intent can be proved).
The circumstances described by k8bailey definitely amount to burglary, even if the offender walked in through an open front door. I have seen cases of burglary being charged when the offender walked into the till area of a shop (during opening hours) with the intent to steal. The law applies because they were trespassing in the part of the building not open to the public.
Whether your insurer will pay up, k8, very much depends on the level of blame they might attribute to you by leaving the door unlocked. As suggested by Jack and boxtops, the “small print” may determine whether they pay. I’ve just looked at the “general exceptions” section of my policy. It says:
“You must do all you can reasonably do to avoid injury, loss or damage and protect your property.”
If your insurers have a similar clause (which they no doubt will have) they could argue that failing to lock the front door contravenes that clause.