I am a single parent and higher rate taxpayer. I am very lucky. When my ex left a few years back I was a scared unemployed single mum with 2 young DC, but I now work full time, in a demanding job, and I make very good money from it. Each year I pay 50% of my income in taxes and I don't begrudge the tax I pay at all. (and I didn't vote this government in).
BUT public finances are finite, so choices do have to be made. Do you fund health, education, social care for the elderly or benefits? Should we give more money to those in the SE or do we need to improve living standards up north? (I live in the north, where I live half the schools are less than satisfactory, and health outcomes are poor). If someone gets more, other services will have less, (I am working on cancer drugs for which there will be no NHS funding as there just isn't the money). In that context a cap is reasonable. Yes it will disadvantage some, but not capping benefits disadvantages a whole host of hidden others.
BUT there are two issues that contribute to the problem that successive governments have not tackled. We aren't building nearly enough social housing, so rents are far too high, and the minimum wage is far too low. If the government is serious about social justice,(and I'm yet to be convinced they are) they must tackle the housing shortage head on. They must also stop propping up the profits of big corporations such as Tesco, or Amazon through tax credits and force them to pay their staff a living wage.
If they do this there will be more money in the system to support those in greatest need.