The key thing a secured lender is looking at is the security on offer and the loan to value (LTV) of the security. A lender will typically lend to a maximum of 70% of the value so as an example:-

Property value: £500,000

Existing mortgage: £200,000

In this instance, 70% Loan to Value (LTV) is £350,000 so a lender would look to offer £150,000 as the £150,000 loan plus the existing mortgage equals the LTV of £350,000.