That Institute for Economic Affairs report seems to recommend a Citizen's Income

From page 172 of this

A flat rate tax plus a lump sum transfer could be optimal

The theoretical ideas behind this are complex. However, progressivity could be achieved by having a lump sum transfer to all people (which would be progressive because it would be a bigger proportion of income for the poor) and a flat tax rate (which would avoid the problem of rising marginal rates).

Correct, how come it’s mainly right-wingers who get this?

From the point of view of low earners, it is the personal allowance/Citizen’s Income which has the biggest impact on how much tax they pay; from the point of view of high earners it is the average rate. For middle earners, it is a bit of both.

So you can keep everybody happy with a Citizen’s Income/flat tax system.