Technically speaking, the cash you received from the factor is in fact a loan and is therefore exempt for VAT purposes. So you do not need to account for the VAT on the debts at the point you receive payments from the factor.
Instead, you account for the VAT in the VAT period the customers pay the factor. The factor should issue you with statements, so that you can identify when and how much the customers pay.
You should account for the VAT on the amount the factors manage to recover; not the original invoiced amount. Please also note that if the factor deducts any commission or charges before remitting you the balance, you should continue to base the VAT on the amount the factor received from your customers; not the lower amount they eventually paid you.