The proposed policy you are describing is akin to a basic International Microeconomics model with free immigration but immovable capital/goods. Assume two economies, $A$ and $B$, where in the one wages are higher, say $w_A > w_B$.
The basic results will be:
1) Immigration flows from economy $B$ to economy $A$ will continue until the wage is equated in both economies.
2) This common wage $w^*$ will be in between the previous two: $w_A > w^* > w_B$. This is because, as labor is concentrated in host Economy $A$ its marginal product falls and so is the wage, while as labor becomes more scarce in economy $B$ its marginal product and so the wage there increases.
The basic distributional consequences will be
1) Workers from economy $B$, both those that emigrated to economy $A$ as well as those that "stayed behind", will have higher wages than before.
2) Workers in the host economy $A$ will see their wage get lower compared to previously.
3) Capital holders in the host economy $A$ will see their returns increase
4) Capital holders in the origin economy $B$ will see their returns decrease.
Introducing a dynamic aspect (capital accumulation, technological progress), would modify the above conclusions in the following way: immigration will partially "hold back" any increases in the host-economy wage, resulting in lower wage increases than what would happen without immigration.
So from the point of view of a host country like the UK is, under such a policy foreign workers (immigrants or not) and local capitalists will benefit, while local workers and foreign capitalists will get hurt.
In my eyes, the above constitute an interesting framework to contemplate the ideological principles alluded to by the OP, but this is a discourse that does not belong to this site.