I don't have a problem with the notion that a representation of the people (not just Tony bloody Blair) comes in to existence to actively monitor this administration's handling of Brexit.
Currently they seem to have moved on from the 'ooh f*ck, it actually happened .. f*ck me ..' stage to the 'ooh f*ck, I err oh I umm' stage and look ready to rush it as a consequence.
Many level headed folk would prefer to see Brexit conducted with all possible due diligence, in the timescale available.

I'm not sure that is what Blair is trying to drum up, but it may help to create such a representation.