Well it definitely won't be Broadmoor, that's a forensic unit for violent criminals with mental illnesses.
More likely you'll be taken to a&e for any treatment you require. Depending on the severity of your attempt and whether or not you have a history of mental illness, attempts or involvement with mental health services, you'll be assessed, speak with psych liaison either discharged home or given a mental health act assessment. There are ways to talk your way out of hospitalisation if that's what they're leaning towards and there is a thread on here somewhere that provides info on that topic. Given the crippling pressure the NHS mental health service is under, unless your attempt is very serious or you have a rich history of attempts and are at high risk, you'll probably be discharged home and be referred to CMHT or the home treatment team or if you manage to say the right things, be discharged home with little more than a report sent to your GP.
