Whether you call VM to give disconnection notice, or to report your service fault, you'll need to call Virgin Media regardless. (Unless you want to serve cancellation notice by post)
Whilst this is a TV-board and broadband speeds are best discussed in those boards, VM's broadband speeds are generally what they are. Any other provider runs over BT's Openreach network where your speeds can vary from address to address.
Get your offer from whichever other supplier it is, lined up and ready-to-go. Call up VM and use the "thinking of leaving us" option, and hopefully for you the agent will arrange the necessary engineer visit/box replacement and get you a suitable new deal. If you're not happy with the outcome from that same call, then you're free to serve your 30days notice and start the ball rolling on your alternative supplier.
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