According to Citizens Advice it seems that you can! They estimate that long standing 'loyal' customers who do not frequently switch to different providers pay on average £900 more a year for mobile phones, broadband, insurance, mortgages, and cash savings.
Based on this research, Citizens Advice have made a "super complaint" to the Competition and Markets Authority (CMA), asking them to investigate this issue.
The CMA has said it will publish a response to Citizens Advice within 90 days, while the FCA, who regulate three of the markets in question, has also promised to look into this issue.
Long standing customers paying higher prices for certain FS products has been an issue that the FCA has been concerned about for some time. In particular, the FCA has worried that the higher prices charged to loyal customers may be used to cross-subsidise more attractive deals on offer to new customers - a concern explored in our recent paper on this subject.
In their response to Citizens Advice, the FCA highlighted its previous work on mortgages and cash savings, as well as its forthcoming market study on pricing in the home and motor insurance markets. So this is clearly a subject where we can expect to hear more from the FCA and CMA in future, and it will be interesting to see what action - if any - the two regulators decide to take.