I'm up for running fibre under the floor and out the property to the front.
Cityfibre won't splice to an existing fibre of yours.
If you can have a conduit with a drawstring already in place *before* the installation day, they may agree to pull their fibre through it, similar to Virgin. There are no guarantees, but if it's done in such a way that it makes their install easier overall, they'll likely do it.
They may also agree to route the external cable around the outside of the house, if that's acceptable to you.
In principle you could join onto their fibre with a SC-SC coupler and a pre-made OS2 (single mode) fibre, but the join would need to be indoors, not outdoors - i.e. they'd drill through the wall and install the ONT at the front of the house, and then later you'd move it and add the extension. However the coupler will introduce a point of unreliability, and if there's ever a problem with your service, they may blame it on that. I would never choose this option.
I agree with the other comment: if they insist on installing the ONT at the front of the house, then run internal CAT6A. (CAT5e would be fine for the 1G ONT you get today, but Cityfibre are planning to roll out XGS-PON so you may be able to take a >1G service soon)
If you want your ONT to benefit from UPS then you can get PoE adapters to power it over the same cable.