Plumbers can replace radiators, install thermostatic valves, install towel rails, and perform a power flush. They also work on bathrooms.
An emergency plumber is a plumber who stops what they're doing and comes to you as soon as possible to fix your plumbing problem. They can get to you in 30 minutes or less. Most want to be open 24 hours a day.
Turn off the main water supply to stay safe and prevent further damage while you wait for an emergency plumber to arrive.
A drain snake could eliminate a clog in your bathtub that won't go away. But if that doesn't work, the blockage may be too far down the line for you to reach.