Have these two bothered to study them? They suggest that without immigration and the children of immigrants (1st/2nd gen are statistically more likely to have children) the UK population would be in decline, in common with that of other wealthy developed countries.
Money seems to be an effective contraceptive!
You could say that someone in the UK has 160 times the carbon emissions of an Ethiopian, then again they probably have a much higher economic output than the typical subsistence farmer - do you choose to put a value on that, or just say that everyone gets an equal slice?.
There is the possibility that eugenics could be dragged into this too; the ones who breed most are typically at the poorer end of the spectrum, so there would be the option that the benefits system would allow certain segments of society to be 'encouraged' not to breed and it could be argued this would be good for society - in other more productive sections of the population lack of income seems to do the job even though you could argue that they should be encouraged to reproduce.
But I wouldn't want to live in a society that thought along those lines.
To be honest some of these people need to realise that 'equal shares' as a concept is never going to fly, it's fundamentally incompatible with the way any organism behaves. Some will always get more, and some will get less.
I suspect if they thought they could get away with it they'd be in full-on fascist mode and advocate culling populations which exceed local sustainability levels - after all if some parts of they world lost a billion or two, the survivors would be so much better off wouldn't they? And just think of the emissions savings...
If they were really serious about reducing global population they'd lead by example - preferably via euthanasia.
Personally I think that giving these kinds of people the oxygen of publicity is wrong. They don't understand the problem, they don't have a solution, and all they do is encourage the real freaks that their ideas might have some value.