Yes, you can ask for it, and you should. In practice, cardiac rehabilitation in the UK is most consistently offered to people recovering from a heart attack. If your cardiac arrest was caused by an arrhythmia, an inherited condition, or had no identified cause, you may not be referred automatically.
You are entitled to ask for a referral regardless of the cause of your arrest. Speak to your cardiologist, cardiac nurse or GP, and be persistent. The supervised exercise, education and psychological support that rehab provides are valuable for all cardiac arrest survivors, and some areas run programmes that accept a wider range of patients.
If you are turned down, ask why, and ask what alternatives are available locally. Our community includes many survivors who only got a rehab place because they pushed for one.