To do this over email?

Email is perfectly fine. For your exact circumstances. If you messed up on the call, as you worry you might, it could really hurt her.

However, you do have the option of writing a script and practising it. Try to think of questions she might have. So, when asked for specifics, just repeat that the email will provide as much clarity as you're able to give. It's a good opportunity for you to practise being direct and dealing with challenging situations.

And if she really did blag the job (can you blame her) then she is likely expecting it. Soften the blow by telling her she will get a great reference.

You need to see her in person!

Nice to hear back. Thank you, and well done

Excellent! We are all very different, however as a fellow member of team email, I’m pleased it worked best for you and her.

As this person is supplier not an employee the aagreement will need to be terminated by email I assume

Emails are cop outs in these situations. I’d make the call (although I hate it) and follow up with an email.

Email so it's on record.

Is the OP coming back or is another one where people invest and don't get a response to their efforts to help.

What did she say OP?

At the very least you should phone her, but I think it would be far more courteous to speak to her in person when she is next due to come into the office. It would be incredibly rude to dismiss her by email.

I've had to address problems after other people perhaps messed up the phone call. Or perhaps the recipient has struggled to process and misunderstood. A carefully considered email is a much safer option, and I would definitely offer a follow up conversation if anyone wanted it.

I've been let go in a similar position (I fucked up, was a well deserved firing tbh) over the phone and 100% would've preferred it over email, I think both of us would've done tbh.

You need to do this the right way, and it's totally unacceptable to let someone go by email.

YANBU
I don’t think there’s anything wrong with a kindly worded email.

If anything you could cause a lot more damage by calling. You could say the wrong thing and she’ll gauge the tone and awkwardness of your voice, which would be excruciating for both of you.

TBH I don't think I would be writing a "kind" email either.
This service provider hasn't provided their services correctly and has cost you money.
I would be stating this as the reason for immediate termination, as they may have a notice clause in their contract - which I would want to argue as voided due to their poor service provision.

Whenever I have to break unwanted news, I write to give them a heads up, state the outcome and the rationale behind it so that they can begin processing in private, but in that letter I offer a meeting time and date to talk. When you cold call people with unexpected news they can struggle to properly listen because they're understandably preoccupied.

You would consider a phone call “unprofessional”?

Because you’re not an expected to immediately digest and respond to an email. On the phone, you’re on the spot and may not quite know how to respond. I’d feel a bit awkward receiving that phone call and would rather have a polite email confirming it.

It’s really not the same. The OP says that she has other clients. It’s totally normal to lose clients on occasion.

I would be bemused and consider it unprofessional to get an out of the blue phone call (or worse, a face to face meeting) for this. Email, with a potential call/meeting would be fine.

I have made a point of doing this sort of thing in person during my career. The first time I had to let someone go, it was awful, and I hated every moment of it. Face to face is the only way, in my humble opinion.

That’s why I said “essentially” because she’s not being made redundant but it’s pretty much the same thing- being told you’re no longer required for a job and won’t be paid any more.

Is it though? My time has still been wasted by interviews and they don’t have the decency to phone me. Like I said, it’s probably best to email her first, then follow it up with a call. Especially if the OP is scared she won’t be able to have the conversation.

She hasn't though, she's not an employee

I doubt it’s an age thing. More people confusing being a self-employed contractor with being an employee (hence comments about her being fired/made redundant, when it’s no such thing).

I’m over 40 and would expect/want an email if my services for contracted work were no longer needed.

You’re correct, technically it isn’t firing as she is not an employee. However in reality if you are using someone’s services and no longer need them, telling them you don’t need them is in essence the same thing (ignoring the technical details). The decent thing, and grown up thing to do, is phone that person.

This person also has her own business and it’s her livelihood. She will 100% want notice to plan but also feedback so she can improve.

How would anyone feel being let go via email with no reason as to why so they can learn etc?