I don't think either of you are being unreasonable, it's such a tough choice. But on balance I feel most sorry for your MIL, as your decision will be very hard on her. If your MIL has had a settled life for a while,.the prospect of change late in life might cause her a lot of anxiety. She is well established where she is, she may find it very hard to contemplate moving, especially if she loves the London lifestyle, it will be very different moving away.
Two hours drive is a lot if you don't drive - it's too much for you to pop round if she is poorly, it's reasonably hard to do as a day trip. There will be no spontaneous visits. How will she be able to come and visit you? I think you need to help her imagine what the changes will be and how she will cope. As otherwise she will understandably feel deserted.
Is there nowhere closer to London you could move to as a compromise?
Perhaps what you should do is take a pause, and ask your MIL to at least consider the pros and cons for everyone involved and think about what happens as she gets older too.
I faced something similar after my dad and uncle died, my mum was alone, and my OH and I wanted to move west. We chose a town we knew my mum would like. We drove her there a few times to see the town centre, the areas we liked. She became comfortable with the idea of moving but in honesty she had always said she would move closer to me if she ended up alone.
It is very hard caring for an elderly relative from a distance, and if you are likely to be in that situation one day you need to think realistically about what would happen. If she refused to leave London will you just leave her to her fate if she gets sick? I have watched ageing relatives become housebound and become a burden due to cancer, dementia etc. You need a long term plan, in my opinion, which your OH should be on board with.