Normally you will have a nil tax code, which will mean HMRC will contact your Finance Dept but they won't advise any reason for the tax code change.
Depending upon your job and your employment contract there may be an insolvency clause so have a look at your contract to check if there is anything regarding BR in it.
Claire, if it is important that your employer does not know pick the correct time of year (jan - March)
however most big employers have staff support sections that may help you through what can be difficult times.
obvioulsy check contract ? it may be worth finding a senior manager / director to confide in then if your BR details gets out it is not going to case you added stress