I’m afraid finding employment in the UK without a degree is not going to be easy. The UK is a highly competitive market for ESL teachers. Your Trinity TESOL Cert is definitely going to be a plus but most schools require a Degree and often teaching experience on top of a Cert.
These schools might also favor a Degree or Diploma from one college (or country) but not another (regardless of the content of these courses). Some employers insist on a traditional on-campus certificate course whilst others recognize the value of online certificates issued by a professional organization.
Basically, requirements vary from school to school so it might be worth making a list of the schools in the area where you'd like to work and contact them to see exactly what their hiring criteria are.