British Psych Wards (Trigger Warning)

Psych ward would be recognisable here

Usually each hospital does general stuff and specialises in something, they won;t have a ward for everything (except in major hospitals perhaps). Until a few years ago we had a psych ward speciality at the local hospital (thanks Blair for shutting that).

So I'd go to A&E in my local hospital, they would have kept me originally (because they had the docs/facilities), but now they'd send me over to he next nearest hospital that specialises

ETA The Priory -- famous for celeb rehab etc and psych stuff -- is in Roehampton. But I'm not sure if they take NHS cases

Wandsworth/Roehampton comes under St George's Hospital area, so she might well end up at St Georges A&E. Queen Mary's Roehampton has only a minor injuries unit, though it does have an in-patient mental health unit, so she might end up there or at Springfield
http://www.swlstg-tr.nhs.uk/contact-us/find_us/springfield_university_hospital/

Beds in psychiatric hospitals are at a real premium in the UK and someone who attempted suicide, but is not otherwise mentally ill might well not be sent to one.

I work for a north-east London NHS trust - there's a specialised psychiatric hospital on our site, not affiliated with our trust, but our in-hospital mental health team often refer patients in need of psychiatric care there for outpatient care. In extreme cases, we do refer patients to be cared for as inpatients, but as Waylander says, beds are very limited so it's usually only very extreme cases that get referred.

Based on a similar case that happened recently (overdose, not cutting of wrists) what would usually happen is that the physical damage would be cared for in A&E or the MAU (Medical Assessment Unit - where patients are cared for before being allocated to a ward, or discharged) and, assuming the acute psychiatric crisis has resolved, they would then be referred to the mental health team for further counselling. After that, they'd be set up with an outpatients assessment at the psych hospital, but that could be weeks afterwards.

Unless the patient's mental state is altered for a prolonged period of time, and they're an active thread to themselves or others, we likely wouldn't involve the psychiatric hospital at all, except in their outpatient care once the patient is discharged.