The consumer group asked more than 5,000 broadband customers whether they had haggled for a new deal or switched in the past 12 months and if so, how much they saved.
Nearly half (45%) of customers said they had never contacted their current provider to ask for a better deal, two in five (38%) had never switched provider and another quarter (24%) had not switched for more than three years.
The majority of those who had negotiated had been successful.
More than three-quarters (78%) were offered an incentive, discount or a better deal.
Natalie Hitchins, Which? head of home products and services, said: "Many of us obediently pay our bills throughout the year without ever giving it a second thought but just one phone call or online chat could save you £120 this Christmas.
"There are bigger savings to be had for those willing to switch to a new provider, but even if you are happy where you are, don't be afraid to ask for a discount - it could make all the difference."
When Which? asked customers who had not recently negotiated with their provider if they were paying more, less or the same as when they first signed up to their deal, most (51%) said they paid the same.
Two-fifths (40%) who had not attempted to haggle with their provider said it was because they were happy with the current price they were paying.
Some also thought haggling would be too much hassle - but among those who had tried it, the majority (52%) found it easy with only a quarter (27%) saying it was difficult.
Seven in 10 (71%) of those who switched provider said the process was easy, even though 27% experienced time without an internet connection as a result.
Which? said that in the majority of cases, switching is straightforward.
Most customers will only need to contact one provider - the company they are moving to - and it will take care of the switch.
This is known as gaining provider-led switching and is in place for all the providers using the Openreach network, including BT, EE, Plusnet, Sky, TalkTalk, Vodafone and Zen Internet.
Which? said those switching to or from a separate network go through the cease and re-provide process.
This means asking the previous provider to switch the old connection off and the customer having to co-ordinate the move to the new provider themselves.
Next year, regulator Ofcom will consult on changes to the switching process with the aim of making the process of changing between providers much easier for customers.