Not mobile only Broadband, around 20 plus years ago when they were Orange there were multiple Broadband issues so after yet another India phone call resolved I told the person this is your final warning, next issue I am leaving.
Thankfully no issues since, phone is with Three
When my Sky renewal came up I flatly refused and then around a week later a guy rang me from India and offered a lower price than I was already paying.
Same with EE and broadband, got a cheaper deal and faster broadband.
NB They get you back as Sky change the price through the contract and EE...