If your Internet connection is via WiFi, then interference is certainly possible.
To communicate between your devices, Bluetooth sends signals over a 2.4GHz radio frequency. This becomes problematic when other nearby devices are also using that frequency. Wi-Fi is perhaps the biggest and most problematic example, as are other Bluetooth receivers and devices, which can interfere with one another.
How to mitigate Frequency Interference :
Remove All Barriers: Certain building materials can get in the way of weaker signals like Bluetooth. Metal, bulletproof glass, concrete and plaster are particularly bad, and marble, plaster and brick aren’t great.
Change Router Channel: Specifically, a different channel than the one your Bluetooth devices are using to communicate.
Connect to a 5 GHz wireless network (if possible).
Move your computer and Wi-Fi router closer to each other, or use wired connection.
As a (not very good) workaround I am unplugging the bluetooth receiver every time I visit a web page! :-/ – EleventhDoctor – 2017-08-03T13:39:25.747
As per comments below, I eventually decided to simply switch to wired mouse and keyboard. Inexpensive and problem solved! :-) – EleventhDoctor – 2017-08-10T16:31:53.950