No. You do not need a VAT number to apply — indeed you do not need to be VAT-registered at all. Plenty of healthy companies trade below the VAT threshold, and that is entirely fine. If you are registered, having the number to hand is convenient, but it is never a requirement.
VAT status is neutral
Being VAT-registered is neither a requirement nor an advantage — the assessment rests on trading history, bank activity and the company credit picture, not your VAT position. This is spelt out in whether you need to be VAT-registered or trading a certain time and whether there is a minimum turnover to apply.
Your company number and registered details, business bank access, and a clear purpose — what company information do you need to see. VAT is not on that list.
If a VAT bill is the reason you are borrowing
Needing finance to cover a VAT bill is a different, valid matter — can i apply to cover a vat or tax bill. Either way, no VAT number is needed simply to apply.
Apply — VAT-registered or not.
We lend only to UK limited companies and LLPs, the loan is to the company with no director personal guarantee, and this is business finance outside the consumer-credit regime — as an exempt lender under Article 60B of the Regulated Activities Order we sit outside FCA consumer-credit regulation, so the Financial Ombudsman Service and FSCS do not apply.
See also: Whether you need to be VAT-registered or trading a certain time, Can I apply for finance to cover a VAT or tax bill?, What information about my company do you need to see?.