Satellite connectivity enables ordinary phones to operate as normal with full internet access when there is otherwise no coverage.
Many iPhones and Android devices already have emergency satellite connectivity, but it is currently text message based.
Vodafone says it has now gone further with a video call between a company engineer in a not spot in west Wales, and Ms Della Valle.
"It's a really important moment because we are opening the door to universal connectivity, to connecting people in the UK, wherever they are," Ms Della Valle said.
She likened the satellites to "antennas in the sky" but said they would not replace existing masts and towers - instead providing an additional layer of coverage.
Phone users will not require any extra equipment, the firm says, as it expands the service.
It does not yet know what the costs will be for customers.
It has partnered with a satellite company called AST SpaceMobile, which has relatively few satellites in orbit - Monday's test had to be carefully timed around one being in the right place, at the right time.
"The challenges really are the fact that it is a relatively new satellite company," said Luke Pearce, from analysts CCS Insight.
"They've got a few satellites up in the air as of last year, but they really need to build out a full constellation to be able to offer consistent coverage all of the time."
Mr Pearce said the issue of how such satellite services would be regulated still needed to be resolved - something that also affects rival providers, such as Elon Musk's Starlink.
Ofcom has previously said it plans to consult on the matter in "early 2025".
