The government is not putting a tax on bedrooms
A tax is defined as follows in the Oxford dictionary:
"A compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions."
It is a tax when you earn money and the government takes some of it, or when you leave money to your children and the government takes some of it, or when you buy something and the government requires you to pay some extra money which goes to the exchequer.
Or in really simple language:
It is a tax when the government takes your money away
IT IS NOT A TAX WHEN THE GOVERNMENT PAYS YOU MONEY.
Not even if, because a previous incompetent government nearly bankrupted the economy, the present government is forced to pay you less than you were getting before.
At the moment we have tens of thousands of households in properties which are too small for them, but we also have a large number of subsidised homes which appear not to be fully utilised. The government is trying to encourage those in subsidised housing which is more spacious than they need to move to smaller homes and free the larger homes up for those in housing need. They are doing this by linking the support paid by government more closely to the number of persons in the household rather than the size of the accomodation they currently occupy.
Pensioners are exempt from this change, and there is a fund which those who have special circumstances as a result of this change can apply for. For example, any family with one or more disabled children whose disability means that they need more bedroom or other space should be able to get help from that fund.
You can make a lot of arguments about the detail of how this policy should work, whether there is enough housing available to enable people to move to smaller units, whether there may be some people like service personnel for whom it may cause problems. Some of those arguments have some force and some of these issues should ideally be addressed. But the change is not a tax of any kind, and to throw around terms like "the bedroom tax" is downright misleading.