What happens if I don’t have a guarantor?

Not all tenants require a guarantor. You will only need a guarantor if you do not meet the income requirements or will/have failed reference checks.
If you require a guarantor but do not have a suitable person to help you, it is up to the landlord to decide if they would like to proceed without a guarantor. Renting without a guarantor is a risk to the landlord, so they may decide to decline your application and choose another tenant.