You do not necessarily need to have lived for 20 years in the UK in order to be eligible to apply for a visa to stay. You can apply for a family visa on the basis of your private life as long as you are already in the UK, and you can prove that you are one of the following:
Under 18 years of age and you have lived in the UK continuously for a minimum of seven years, and it would be unreasonable to expect you to leave the UK
Between 18 and 24 years of age and you have lived continuously in the UK for more than half your life
18 years of age or over, and you have spent less than 20 years in the UK, but would have very significant problems living in the country you would be required to go to –for example, you do not speak the language and would be unable to learn it
At least 25 years of age, and you have been in the UK continuously for 20 years
Your family members will also be able to apply on the same application, although the Home Office will consider you separately.