No as the arrangement between BT and other ISPs is a wholesale carrier one where they supply the DSL only and backhaul the traffic to an ISP's edge router.
Fon is a BT Retail product only.
Virgin (ADSL) => Namesco => Newnet => O2 => Plusnet => Zen => Newnet => Zen => Freeola => Vivaciti (using O2 Wholesale DSL) => Xilo (C&W Wholesale) => Xilo (O2 Wholesale)
Note: I don't lay turf for anyone. astro or otherwise, all views and opinions expressed are my own based on experience.