If you are thinking of camping outside Downing St you'll be wasting your time.
If you want to camp out anywhere to draw attention to a specific case then camp out (or even better stage a sit-in) at your Local Authority offices.
The law is there for you to use. You don't need to be a solicitor - just research and understand your Council's statutory obligations to you and make your case and put it to them.
If they fail to act reasonably then report them to the Local Governemnt Ombudsman.
You don't need a solicitor for that. You just raise raise a Formal Complaint through the Council's complaints procedure and, having exhausted all 3 stages of the process, you can tkae your case to the LGO.
I did this without a solicitor and won my case.
I'm not saying it's easy - hours / days of research are needed and a considerable amount of time spent developing your arguments for the LGO to consider.
In my LA they are now building autistic bases - Why? Because - and I quote the Minutes of their education services meetings - it's cheaper than having to fund expensive independant provision for the increasing numbers of children whose parents are taking the Council to Tribunal to secure an appropraite placement for their child.
That's grass roots politics producing a meaningful and achievable outcome.
We should do the same for carers. Apply for a statutory assessment of the Child's needs under the existing provision of the Children's Act and request a similar assessment of the carer's own needs.
Disgree strongly with the very weak identification of needs report they produce. Raise formal complaints and take each case forward. They'll soon get the message - that it costs less to address needs up front than to get tied up in paperwork / legal process to deny care.
That's how I woudl tackle the issue.
But if you think camping out in Downing St is the way forward - whatever.