If you are in an authentic and constant-relationship and have child too, you may be able to speed up processing time. A long-term relationship is defined as someone who has been with you for at least 2 years or 3 years when you have a child.
Common-law [relationships of at least one-year]
If you are unmarried, but living-together, then you must prove that your relationship is real and has been going on for at least one-year.
You will also need to provide proof for the same. Proof can be joint finance, alikeness like email, chat etc., the time or past of your relationship.