In reply to a post by RobLittler:

Today I have learned that little white box is a fibre ONto the home Terminal.

It's an Optical Network Terminal (ONT) or Optical Network Unit (ONU).

The chassis in the exchange at the other end is the Optical Line Termination (OLT)

Pulse8 offer service without providing a router (they charge an additional fee, should you require one).

Though a potential issue is that it sounds like you have or are ceasing service with EE altogether rather than just migrating service to another ISP.

If that's the case, Pulse8 charge a £80 service activation fee, which they waive for migrations

Whether the ISP supplies the router is neither here nor there. It really doesn’t change the price you pay.

Virtually all Openreach based FTTP service providers will allow you to use your own router. If you are supplied with a router from the service provider, just keep it in the box and return it at the end of the agreement. No big deal.

Personally I would be concerning myself with other criteria upon which to select an ISP and whether they omit a router is as noted pretty inconsequential.

it's irrational, but this is what I seem to have found, it makes no sense, all I want is for someone to switch on the connection to the property, but they insist on sending me a plastic box every couple of years that comes with a crapton of restrictions if I use it.

I guess that is the way of the world. Olilo is exactly what I want in an ISP, but it costs more than if I just take the damn plastic box.

Thank you all for your replies, but I think that concludes this foray.