Wendy, please ignore the comment from the anonymous first poster, I honestly think that was well out of order.
F451 raises a good point about claims taking some time, but I gather from your comments about payments being stopped, that this is not the case this time. As for not renting to non LHA, it's going to be difficult to be able to terminate your tenancy if they lose their job after having moved in.
I'd rather you didn't stop renting to LHA tenants as there is going to be a growing demand considering the current economic climate, but your reaction is not too dissimilar to those that we saw a few years ago in the early 80s and early 90s, when we were in a similar situation.
I can't offer advice on your current situation, but if you're willing to rent long term, you can consider approaching a housing association, who will sign a fixed term contract to pay you rent whether the property is let or void, and will have to agree on the standard the property can be returned to you. The rent might not be as high, but it takes the worry and the hassle out of it for you.