You might be referring to Dr. Peter Hammond. According to his study, the tipping point seems to occur when Muslims are around 5 to 10% of the population. That’s when they stop smiling and start demanding local Sharia law.
The UK is now roughly 7% Muslim.
Dr.Hammond‘s study is here:
https://virtueonline.org/what-islam-isnt-dr-peter-hammond
They're mostly concentrated in London, which is the political, cultural and economic capital of the UK. So they're making their presence known already by electing a Muslim mayor.