The bedroom tax is not a nudge.
Cultural note: UK has a benefit called "Housing benefit". It pays rent for people in certain circumstances. Years ago people renting from a private landlord had limits imposed about the size of property they could rent - they were not allowed to be over accommodated. (Or they could be, but they wouldn't get that rate for the property and they'd need to make up the difference). Recently this rule has been applied to people renting from the public sector - local council housing and housing association properties.
In theory it creates liquidity in the property market, and makes sure people are in the right size homes and getting the right amount of benefit. In practice people who can only afford to live in council housing cannot afford to move, even if there were other properties available for them. (And there usually aren't, and even less so now that so many people are looking to move.)
In this situation a nudge would be finding the sticking point of why people stay in properties with too many rooms and finding a way to help them move. Offering to ebay extra possessions, allowing them to fit into a smaller home, would be a nudge. Offering help with removal vans or other logistics might be a nudge.
Cutting benefit to poor people is a kludge.