They can demand but the likelihood of them getting anything good is low. For the ultra paranoid, spin up algo vpn https://github.com/trailofbits/algo on a droplet hosted out of reach of the UK and recycle that droplet on a regular basis. Logs take up space and VPS providers don't save for long, so the time it takes for a warrant to be produced, the chance of logs being there are slim
They can demand but the likelihood of them getting anything good is low. For the ultra paranoid, spin up algo vpn https://github.com/trailofbits/algo on a droplet hosted out of reach of the UK and recycle that droplet on a regular basis. Logs take up space and VPS providers don't save for long, so the time it takes for a warrant to be produced, the chance of logs being there are slim