Just to highlight the problem with not reporting to Equifax, it appears they are the primary CRA used by mobile networks and indeed some including BT, EE, Virgin Media and Tesco Mobile use them exclusively.
Info from Ocean Finance at the link below - page also has details of what CRAs are used by banks, loan and morgage lenders.
The data may have changed since that report, certainly prior to CallCredit changing to TransUnion.
A quick Google on BT
We use data held about you by these two credit reference agencies:
Experian
EquifaxIn return we make a record of how you conduct your account. This information is provided to the agencies automatically each month.
And EE is
We use customer data held by these three credit reference agencies:
Experian
Equifax
Call CreditIn return we make a record of how you conduct your account. This information is provided to the agencies automatically each month.
Tesco Mobile have two by your own list? 
Oh silly me, think I had my blinkers on looking at Experian and Equifax. Even so, does seem there is a trend of mobile networks using Equifax as first point of call.
Just checked my equifax, according to them I don’t have a current account despite having both Monzo and Natwest accounts.
Only thing that shows is my Amex, Tesco Foundation Card I used to build credit and my 3 sim only plan.
Doesn’t really bother me.
Just received an email from Monzo with updated terms and conditions. In it, it mentions working with Equifax.
More information here: Monzo – Customer Privacy Notice
If you sign up to a service from one of our partners through the Monzo app (like energy switching or remortgaging),
I’ve had both of those offers in app. I took them up on their energy switch offer. Are they still doing this?
I thought the remortgaging was a trial and they’d have removed that by now. There’s still hope of a marketplace
Energy switching isn’t available for northern Irish customers so no idea what’s happening with that
The remortgage was a trial and it hasn’t been available for a while.
Switching energy providers is still available in-app:
I can’t remember 
I hope it is the sign of a marketplace though. It has been very quiet on that front.
Edit. Oh just seen @davidwalton post 
From the email:
We work with Equifax as well as Experian and TransUnion
Before, we only used credit reference agencies Experian and TransUnion.
This is fantastic news if it does mean Monzo are now reporting to all three credit reference agencies: Equifax, Experian & TransUnion. Or maybe it means they plan to very soon?
I’m just aware when they started reporting to Experian they did a blog post about it as big news so I’m surprised they haven’t made an individual announcement.
Would be wonderful if a Monzo staffer could confirm.
Will likely still be a few months away.
Awesome news 
I know some people will be outraged that their personal data being given away to another credit reference agency and they will want some form of opt out. Is that also on the cards or is it mandatory?
You want a toggle for that?
Yeah why not, the more the merrier 
I seem to recall the last time people brought up credit reference agencies it was a mixed bag of people welcoming it and others dead against it.
If I had a choice then I’d rather not, but since I don’t then I’ll live with it
Guessing in the way the CRA’s operate they require banks to not allow customers to opt out otherwise the CRA’s would be pretty data sparse.
Would be nice to have the option for those that want to opt out.
I’d only opt out of equifax beacuse of erm that big data breach they had in the US.
The opt-out can be conditional on having an account in good standing. Obviously opting out while defaulting on your bills shouldn’t be allowed, but provided you pay everything on time (or not have an overdraft/loan on Monzo), I don’t see why not?
