Hi, you sound like you have a good therapist there.
NHS help can vary - at one end you have the talking therapies referred to by the gp, usually limited to 6-8 sessions, sometimes individual othertimes in a group. I would not think this was going to add to anything you already have. Longer term decent talking therapy like you are already receiving tends to me hard to get and it can be confusing to do two different therapies with two different people at the same time, NHS and private. Also you do not get to choose who you see on the NHS and it is usually limited sessions.
Medication is one good avenue to explore with the gp - they often suggest counselling first but you have that. Sleeping tablets, diazepam type medications for short term crisis or specific problems. A whole range of antidepressants depending on the presenting issues. Also anti anxiety medications. Things like sleeping medication and diazepam type drugs are usually given short term as: they are addictive and do not work if keep taking them in longer term. Antidepressants come in many different types and have different uses. However if someone does not have depression, then not sure they would be useful.
Othe rsupport from NHS tends to be linked to your risk rating. Some people with severe mental health issues are referred to a community mental health team for: diagnosis, assessment and they may get regular meetings ( once every 3 months for eg to review medications if on several), or have a community worker - a nurse, a social worker or an occupational health worker. Some people get additional support, such as a family worker or support assistant to help with getting out of the house, caring for themselves practically or for their children ( though this usually comes as a result of a social care assessment and funding). Risk rating will be assessed every six months, to see if extra intervention required ( and to consider safeguarding issues - with children, are you a vulnerable adult that requires additional support etc...).
If under a CMHT they can refer to crisis teams although this depends on where you live as to provision ( a few people get 24 access but not usual). This means when at risk of hurting self or others a crisis team worker can phone to visit daily - nb it is rarely the same person each time and can be at random times depending on how busy they are). It is not therapy, not long term and has no continuity for a patient as that is not its purpose.
Other support could be a referral to a psychiatrist for an official mental health diagnosis if the gp cannot diagnose. For conditions such as bipolar, schizophrenia, personality disorders etc. they can then liaise with your ooupatibal health for risk assessment and making adjustments in work if needed.
You can get support of a crisis team other ways though: by presenting at hospital for mental health assessment, by police or ambulance or social services being called by others, or by going to a gp or out of hours service and they thinking you need a mental health assessment doing or short term intervention.
With medication, they cannot get rid of crap, sadly. Nor can they change how we think or react - that is work you are already tackling with your therapist. They cannot take away life events. For some people they help numb them a bit as feelings can be overwhelming. For some people they are depressed and they help with moods etc.
Other things that can help are more natural:
Fresh air/daylight/exercise helps with low moods for many people
Healthy diet, fluids
Routines - good sleep hygiene, enough rest but not spending too long in bed either
Work - for many people, having positive distractions can really help, so not totally in a " mental health bubble" if that makes sense. Or for people not working, hobbies, volunteering, activities and routine.
Sorry I wrote lots. Feel free to ignore!!