In the UK, there are four dominant carriers, O2, Vodaphone, EE and 3. All of the other carriers piggyback on those four to some extent, for example Tesco Mobile uses O2 as a carrier.
I have a number of SIM cards from sip2sim.uk which connect a mobile device to a VoIP service, which can be provided by their parent company, or any other VoIP provider on the planet. The SIM card itself does not provide a mobile telephone number, as the VoIP service does that. The mobile phone then becomes a registered device on that VoIP server, and consequently could be an internal extension on a corporate network, or any other kind of service provisioned via VoIP. The sip2sim servers just need, for each card, a server, username, and password. What happens to traffic after that point is down to the server you are logging in to.
These SIMs by default piggyback on UK O2, however in the event of no O2 signal, can switch automatically onto Dutch Vodaphone. Why Dutch? UK Vodaphone customers cannot roam onto EE's network, however Vodaphone customers from other countries can, so I effectively get three-network domestic roaming. Quite what will happen after Brexit, I have no idea.
My VoIP service is provided elsewhere, and I have all of my SIMs logging in to that, which means all of my devices have the same telephone number. This seems to confuse some organisations, but the practical upshot is that if you phone my number, you get me. I actually have multiple numbers, some of which I give to work contacts, others to private contacts, others to potentially spammy outfits, as numbers are cheap (as little as GBP 0.10) and can be terminated easily if a specific company starts to annoy me more than most. (British gas, I'm looking at you...)
One downside is that I have a UK telephone number which does not start 07. Numbers starting 07 in the UK are usally mobile telephone numbers, and despite many mobile networks actually offering non 07 numbers, quite a lot of companies think they are doing you a favour by refusing to accept 'mobile' numbers that do not start 07. The conversation usually goes:
Can I have your mobile number?
Sure, it's 014....
No, your mobile number
Yes. 0, 1, ..
No, it starts 07
No it doesnt
Yes it does
Stop asking me for my mobile number and then telling me that it's wrong!
(The conversation usually ends badly at this stage, although sometimes I actually get someone order a SIM card. Just don't get me started on the reaction I get from Carphone Warehouse staff when I try and buy a new mobile handset and they ask what network I'm with. (I just lie, it's easier))
So, I could allocate an 07 number to it, I do have an allocation, but why would I do that as it is still expensive to call 07 numbers from quite a lot of phone contracts when calls to landlines are practically free. (Ok, it's not a landline either, which just illustrates how easily confused the telecoms companies are)