If you have been in UK for 14 years+ without papers, Please find below a link from Home Office regarding application for indefinite leave to remain in UK after 14 continuous residence.
Please find a good immigration lawyer and seek further advice.
2 CRITERIA FOR RESIDENCE
2.1 Criteria for residence for 10 years long residence cases and 14 years long residence cases
Paragraph 276A of the immigration rules defines continuous residence and lawful residence.
To be granted ILR following 14 years long residence, the applicant must meet the criteria for continuous residence for the whole period.
Does the applicant have at least 14 years continuous residence?
Are there any reasons why the granting of leave would be against the public good?
Does the applicant meet the Knowledge of Language and Life criteria? (this is necessary for ILR applications not LTR applications).
3. FACTORS TO BE CONSIDERED BEFORE LEAVE IS GRANTED
3.1 Background
Possession of the required period of residence in the UK does not automatically entitle the applicant to a grant of leave, but only to be considered for a grant. The factors highlighted below should always be taken into consideration when making a decision on a case. However, the general rule is that a person who satisfies the appropriate continuous residence or continuous lawful residence requirement should normally be granted ILR, unless a grant would, in all the circumstances of the case, be against the public interest.
Paragraph 276B(ii) sets out a number of points which should be considered in all cases. These are:
age
strength of connections in the United Kingdom
personal history, including character, conduct, associations and employment record
domestic circumstances
previous criminal record and the nature of any offence of which the person has been convicted
compassionate circumstances
any representations received on the person's behalf
http://www.bia.homeoffice.gov.uk/sitecontent/documents/policyandlaw/IDIs/idischapter18/longresidence/Long_Residence_IDI-_final_d1.pdf?view=Binary