It is normal procedure for a local authority where council tax is owed to first obtain a liability order from the Magistrates court and then to commence action by placing the alleged debt with bailiffs, under normal circumstances once the alleged debt is placed with bailiffs the LA with not take the debt back.
You are quite correct that the type of bailiff you are dealing with do not have the authority to make forceful entry but bailiffs have been known to use many dubious means to make peaceful entry a very popular way is saying “you do not want the neighbours to hear, let us go inside and have a chat” they can make peaceful entry through a window or door which is unlocked. I am aware of an instance where a ladder was used to gain entry through a window and where entry was obtained by going through a garage where there was an internal door to the house. Once peaceful entry is obtained the bailiff will produce a walking possession order which is a list of the items intended to be sold to repay the debt, there are many items they are not permitted to remove, you will be asked to sign the WPO if you do not goods may be removed if you do the bailiff can then make forceable entry on a later visit, the theory being that they are now recovering their own goods. The most important lesson to be learnt is to refuse entry to the bailiff.