Well a huge proportion of immigrants in the UK aren't even receiving minimum wage, working in the grey/gig economy they'll be getting well below minimum wage in reality.Cheap labour abroad doesn’t affect UK productivity they are abroad if you mean people from aboard working for low wages in the UK there is minimum wages and they are being replaced by machines anyway as show in the earlier comments with the ordering machines
Those ordering machines are a rare example of a corporation bothering to invest in technological innovation to improve productivity though, for the most part they just stick with the easier option of exploiting cheap migrant labour.
As I've previously said, comparing "productivity" between different countries is as utterly pointless and meaningless as comparing official GDP figures between different countries.