I think I just used Recorded Delivery for my last passport application, which included my old passport and a cheque.
But, when I applied for a driving license in 2008, I sent that by Special Delivery as the application included a postal order to cover the cost of the application (about £45 if memory serves). Normal post wouldn't have paid compensation if a postal order was lost in the post, as I beleive it is treated like cash (which is covered by Special Delivery).
I have received valuable things, sent cash, and both sent/received important letters using normal postal services and had very few problems.
I think the problem is usually the recipients of letters who seem to conveniently file them away in the dustbin shaped filing cabinet. The local benefit office seems good at this, but they are certainly not the only ones.