Can I stay with my current telephone / broadband supplier?

This depends on which supplier your community chooses for the solution.

If the community choice is Openreach, then your choice of telephone/broadband supplier is more limited than your current choice via copper lines.

If you are currently with BT, EE, Sky Broadband, AAISP, TalkTalk, Vodafone, Aquiss or Zen Internet, then YES you can stay with your current provider. There are other niche providers to choose from:

https://www.openreach.com/fibre-broadband/fttp-providers

If you are with anyone else (such as Plusnet, Virgin Media, Vodafone, SSE or Post Office) then you will NOT be able to stay with them at the moment. However, these providers should become available over the coming months and years.