If you / they are a student at LSE:
The LSE Students Union (SU) has an advice service that can offer online and in-person appointments. They can be contacted by emailing su.advice@lse.ac.uk - please provide an outline of the issue in your email.
There are also other forms of support that LSE and the SU can offer, such as financial assistance in some cases - you can read more about these clicking here.
LSE also has a wellbeing service for students that provides support more generally, including counselling services and a 24/7 mental health support line - you can find out more by clicking here.
If you / they are a member of staff or not part of the School
LSE has a Benevolent Fund which can offer a financial safety net providing relief to members of staff unexpected financial pressures, which you can read more about here. Members of staff can also access wellbeing services which you can access here.
You can use this link to find your/their local council, which is responsible for supporting those in their area who are, or are at risk of becoming, homeless.
There are also a number of different charities that focus on homelessness. Shelter has an emergency helpline - 0808 800 4444, open Mon to Fri, 8am to 6pm - that can offer advice, including to those who need an interpreter or are deaf or have a speech impairment. They also offer housing advice more broadly, which you can access here.
Other charities that offer support include St Mungo's, Centrepoint, and Crisis.