Yes, you can rent a property through flatfair without a credit history, provided you are able to pay your first three months' rent to your landlord upfront, along with your one-off flatfair membership fee. You'll then need to pay your rent in quarterly instalments throughout the year.
For example, if you're renting a property that costs £200 per week (or £867 per month), you'll need to pay your membership fee (one week's rent plus VAT), totalling £240, to flatfair. You'll also need to pay three months' rent (totalling £2601) directly to your landlord, upfront. You'll then need to do the same every three months, throughout your tenancy.