Welcome to the Forum! Great to see you both here.
For some friendly banter and over-the-fence chat - try: https://forum.carersuk.org/t/roll-call-january-2024/124289/369 Roll call is an everyday chat, @susieq starts a new thread each month
@SimonA could you share a little more about your situation - are you living with your Mum in your house, her house, 24/7? Do you have family support - siblings, aunts, uncles, or any friends / neighbours support? what’s the current situtation with the GP practice - like @Michael_1910123 has asked do you feel supported (You yourself, and also with respect to your Mum) in terms of the medical people or any other ways? It’s good to share a bit more as it sounds you’ve already been caring for your Mum for a while?!?!? Only share as much or as little as you want, I’m only asking so I don’t tire you out having to explain or justify what you’ve already done!!!
As @Teddy123 says you’ve started a more pointed conversation - which is NEVER easy and there’s no easy way to broach the topic or make sure it is a success. There’s no such thing. We’re all human, feeling fears, anxiety and a whole host of stuff which - unless we were telepathic - is impossible to fathom outside the person’s head! On top of that our parents are a different generation who are conditioned by a whole host of expectations which are VERY different from your/our/my generation 
AND on top of that whatever Mum-Son dynamics you had will play out - whatever story-baggage you have or she has… So Sorry to lay all that out but I wanted to highlight that you’re doing the best you can - and that’s already sounding like a LOT - and unfortunately, you need to recalibrate your expectations on things…
What I mean is you can’t stop mismatched thinking between her and you.
Like @Teddy123 mentioned it’s worth getting a Needs assessment done, if you haven’t done that already - perhaps an objective assessment from a 3rd person can offer her more food for thought? Although, she may flat out refuse the need for one…
Perhaps you can share if she has any cognitive issues, can you share more about her ailments?
It’s really tough when you’re worried and you want to keep her safe. From her perspective, she may be feeling frustrated she can’t do things she used to do, and impatient with herself and grieving the loss of her youthful abilities…overlay that with - if she’s a strong will independent lady - becoming beholden to others for help, or losing her identity as a strong capable women…then later comes a feeling of being ‘jailed’ into doing things you want …I’ve seen/felt this line of thinking from my Dad but also other carers.
May I suggest that you don’t make a plan and try to persuade her to do it, instead open the follow-up discussion with questions, be curious with open ended questions and leave plenty of time and space for her to find her words. Try to avoid the absolute practicals of money, will writing…and stay in the lane of everyday activities, going to the library, getting around… (you’ll be surprised - or not - at how some gentle questions can get twisted into accusations about money-motivations etc etc).
BUT here’s where us, understanding your situation more fully is best - how ‘safe’ is she, are you in the house, getting around etc? How’s her mental capacity?
medical safety, emotional welfare and well being are not small considerations.
Hope that offers some food for thought and empathy!
You can only do the best you can. She sounds like a wonderfully strong lady who is becoming more aware and frustrated. Sending best wishes to both of you.
FYI
I started helping my Mum look after Dad in 2015, whilst I was working, then I resigned and helped them full time. Dad had numerous conditions heart failure, rheumatoid arthritis (so a lot of mobility issues) and bladder cancer and Vascular dementia. When things were at their worst end of 2019, Mum was diagnosed with 2 separate primary cancers. I took care of Dad full time (toileting, shower etc etc), and supported Mum through her investigations and cancer diagnoses. We managed to fulfil Dad’s wish to die at home (despite paramedica calls at least once a week in Nov & Dec 2019…). Jan 2020 we managed through the funeral service things, and then 16 days later Mum had her first surgery. so not a covid year for us but a Cancer year.