My answer is that I experienced the reverse of what you're talking about, although not exactly the same situation.
My mother lived, until her move to the care home in February of this year following a stay in hospital, alone, with no services, 100 miles from me (about a 1.5 hour drive). When it became clear during her hospital stay that she would need to move to a care home, I was persuaded to consider moving her to the city where I live. The social worker at the hospital said that sooner or later I'd need to be closer to her, to take care of things, and I might as well get all the upheaval over with all at once and make my life easier. Since I had been averaging 2-4 visits per month for the past couple of years, I listened.
Even though it wasn't a very long drive, it is a huge relief not to have to make that drive every single week (although of course, that's exactly what my husband and I have done for months, to clean out her house, but that's another story). I am only 15 minutes away now and yes, it's helpful to be nearer.
This is not to say that you cannot be a long-distance carer. Many people do it and a great deal of the work I do (phone calls, paperwork, bills, financial management) could certainly be done long-distance. If you are intending to be a hands-on caregiver, then you would need to live closer.
I will caution you to think long and hard about personally taking on caregiving. My understanding is that in the UK, no one can be forced to do this. While there are many arguments to becoming a primary caregiver, it all depends on the person and the family and the situation. You do need to know, before you start, that caregiving, hands-on or otherwise, can eat up as much time and energy as you give it, and more, if you don't set limits. Have a read in the various threads here to get an idea of what it's like for different types of carers. (I mean this in a non-judgmental way: each of us has to do what works for us and our families.)
It might also help if you have an idea, before you start, of how much of your time, energy, and money you are willing and able to give to caregiving. Perhaps you have a physical issue (mobility or injury) that would prevent you from lifting someone off the floor or transferring them from a bed to a wheelchair, and so you would need help with that. You might or might not be comfortable handling issues with toileting and incontinence. You may be rubbish at cooking, or hate housecleaning, or unwilling to oversee medications, or a rotten gardener, or maybe you would love doing those chores. Only you can answer those questions.
Best of luck to you.