I won't ever download it. If my gym demands I use it then I'll quit membership. Enforcing that customers use this app in gyms, pubs, shops, etc. is a good way to wreck what's left of the British economy. I doubt that will happen in practise because anyone without a smartphone or anyone with an older smartphone can't download the app so it's of limited use.
Could I ask why? Assuming you carry your phone around with you most of the time, it provides a useful tool for tracing your contacts should you or someone you've been in close contact with become infected. It's non-intrusive, non-centralized (the data remains on your phone until you choose to upload it), and could contribute to reducing the spread of the virus, which could well end up killing a susceptible person. That person might be someone you care about.
The whole point of tools like this is *help* to open up the freedom of movement and keep economic and social activity going, not prevent it.
It doesn't have to have 100% adoption to be effective, so the fact that not everyone has supported smartphones doesn't mean it's useless.
Be socially responsible, and do your bit to help to potentially help others.