To be eligible for quick payday loans in the UK through onlinequickloans.co.uk, applicants must be over 18 years old, a UK citizen with a mobile phone, email, and bank account. They must also have a job and steady income, as payday loans require a source of repayment from one's paycheck. The website offers quick payday, same day, and instant payday loans for those who meet the basic eligibility criteria.