Tube fare is pretty cheap - you can google fare calculators to work out what it will cost for particular journeys, but it’s usually just a few pounds and there are daily caps. Unless the taxi journey is very short, a taxi, especially multiple taxis in one day, will be more. However I still think it’s probably your best option.
A couple years ago I spent several months on crutches due to a serious injury. Something I learned during that time was that if I wanted to take the Tube, it was best to avoid peak times. Off-peak was fine, but at peak times the train cars can get really crowded, and I was honestly shocked how apathetic people seemed to be to a woman balancing on crutches. Very rarely did anyone offer me a seat, and I was routinely buffeted around as people crammed into the car. I can’t imagine even attempting to fit a wheelchair onto a train during rush hour, it simply wouldn’t be possible. So that’s something to keep in mind if you do try the Tube - morning or evening commute times, or prime time for heading to a night out on the weekends or to sporting matches and the like, are not the times to try it! Having moved here from a city where the metro is an absolute shambles (DC), I love the Tube overall, but it was a nightmare when I had mobility issues.
I think accessibility is sadly an area where London really could and should improve a lot. On the bright side, lots of cabbies are very chatty - look at those rides as an opportunity to talk to locals with a unique perspective on the city.
Also - I think you’ll have better luck with black cabs than with Ubers, because of the way the interiors of black cabs are set up to be more spacious. Particularly the van cabs will be good for when your grandson is using his wheelchair. Ubers tend to be a bit cheaper but I like to support the local cabs and they are generally much better about knowing the quickest route somewhere. I use the app Gett if I’m somewhere where I can’t just hail a black cab on the street - it allows you to order a black cab on demand much like the Uber app. There is a surcharge as compared to just hailing one on the street though.