No, almost all broadband providers (with the exception of Virgin Media) will need you to have a landline as this is how broadband is delivered to your home by any provider using the Openreach network.
If you have access to superfast speeds, broadband travels along fibre-optic cables from the exchange to a cabinet near your home. It then makes the journey from the cabinet into your property using a copper phone line. This is a process called fibre-to-the-cabinet (FTTC) broadband. Most homes with superfast broadband have an FTTC connection.
The only major provider that doesn’t require a phone line for installation is Virgin Media, which uses its own network of coaxial cables to deliver broadband. You may also be able to get landline-free broadband if you have access to fibre-to-the-premises (FTTP), also known as full fibre. This delivers broadband directly into your home using fibre-optic cables and bypasses your phone lines altogether.