To do this over email?

As others have said, I’d call and follow up with a formal email to clarify.

Email for sure. I wouldn't want a phone call with this type of news.

Neither - you do it to her face on the day she is in

If you have been repeatedly/persistently unhappy with her work, is it really going to be "out of the blue" though?

I think a lot depends on whether she's self-employed (freelance) or employed by you. Your post isn't clear. You owe a better, fuller conversation to an employee than you do to a freelancer - I say this and I am a freelancer of over 15 years. Part of the freelance life is that you come and go, but if you've employed this person, she needs to know why you're letting her go. The third option is if she is self-employed but has signed a fixed-term contract, in which case you may need to pay her off.

I would hate this to be done in a phone call if I was the one being let go. Email first and a “call me and we can discuss further if necessary” is absolutely fine. Give her a chance to digest the news properly rather than ambushing her with a phone call out of the blue.

Does she do any work for anyone else? Because if she’s just working for you then she’s not self employed.

Self-employed person here! (Also reluctantly so through circumstance, so huge sympathies with your predicament!)

@WellErrrr I would MUCH PREFER an honest and direct email with some feedback/rationale for why you no longer want to use my services than a phone call.

This person is not a member of staff, she's a service provider, so the relationship is not the same. You're not their boss, just a client.

I also think if I were in her shoes, I’d prefer to be given the heads up a month in advance, ie tell her the work is winding down via an informal call at that point.

but now you’re at the point where you’re relinquishing her, it’s too late to give her the heads up. So now there’s no benefit to having the call vs the email. I’d prefer to get the information in this scenario over email so I can process it privately.

if I was a contractor or whatever, I’d be right on the phone trying to secure new opportunities. I wouldn’t want to awkwardly stay on the phone with the client who doesn’t want my services.

Just email if that works for you, there are no firm rules. If you think the call may get difficult safer to email.

I would be gutted if I was sacked by email.

Is there a reason I'm missing why the only options are by email or over the phone? You say she comes in one day a week? Surely in person should be the preferred option?

Another problem with email is that she’s already proven herself to be inefficient. What if one of the things she’s lax about is picking up emails? It would be terrible if she turned up for her office day not realising you had ended the agreement. With a call there’s no ambiguity.

I hate phone calls, and would much prefer an email. I don't know why people always insist you should call someone, not everyone wants that.

She is not an employee, she is a supplier whose services you have used and no longer want to
Be professional and suger coat it a bit if it makes you feel better but its purely a business decision so approach it like that.
Email is fine

I’d just email tbh.

Don’t call unless you’re comfortable answering questions that she may have on the spot. Unless you’re really good at saying I will check and come back to you.

She might be fine, or she might be upset, or she might want to agree a reference etc. I’d personally rather deal with whatever her reaction may be via email.

An email is absolutely fine..just do exactly what you planned to do. It's a business arrangement and can be dealt with it like one.

I don't have any advice really. But I just want to say how refreshing that someone is so considerate.

You need to call but prepare some phrases so that you do not get sidetracked. “Unfortunately we are not finding your work as useful anticipated”, “I understand what you are saying but this no longer works for our business”,” I am giving notice today that as of x date we will be terminating the contract and you service will not be required”(and send an email confirming this), “I am sorry you feel that way but my mind is made up”., “I will confirm this conversation by email”. Try to keep it brief and bring the call to an end if she starts digressing.

Your situation/feelings/how you got into this isn't the issue here. It is about her.

"Hi Jenny, I am calling to say that as of DATE, we will unfortunately not be needing your services any more. I will follow up with a written confirmation for your records. Thanks for your work to date."

She's probably not going to want a long chat after that anyway. But if so, make sure its at a time where you can conveniently have another appointment to go to in the next 5-10 mins.

Kindly - suck it up.

Nothing wrong with email imo

I work in a similar way. Due to funding I am "let go" on occasion I'd ALWAYS prefer an email and it tends to be how it's done

To be honest although I said best to call it is also acceptable to email, if you are really uncomfortable with phone call then put everything in writing over an email and say she can call you if she has any questions