I was on another thread where some posters wanted affordable housing in big cities like London to be only for keyworkers and people who 'need to be there'.
I imagine older people from those cities feel unwelcome and pressured to move away. Especially as (I think?) there's even an official scheme in London to 'relocate' retired social housing tenants to rural areas.
My previous posts on this thread point out many pensioners are in poverty, and many don't own their home.
A significant minority of older people are private renting especially in big cities. Moving away could be their only chance to buy, or to simply continue affording the rent when on a state pension.
Most older people who move away from cities don't buy big houses. Lots, probably most, downsize. They sometimes opt for somewhere less urban, because the more affordable housing in urban areas tends to be tiny flats not designed for older people especially those with mobility needs.
There's been funding cuts to public services across the country. Sometimes support in cities is worse than rural areas, as support schemes there often focus on the young.
Also in cities, many older people's kids have had to move away (due to unaffordable housing). So the issue you mention, of lack of social contact, care including help getting to doctors, and isolation is a problem in big cities too.
Sometimes it's worse, especially as there's less informal community support in large cities because of more transient populations.