Even the gift element should really be disclosed to the lender as it is not
coming from the buyer's own funds.
Lenders do not like any further borrowing than theirs that could be secured over a property.
Depending on how much you would be lending, your son would effectively be borrowing up to 100% of the purchase price so with early redemption penalties and other interest and charges could be immediately in negative equity.
If there is another lender who can force a sale then it prejudices the mortgage lender's position as to what they can recover.
It also isn't a good indication of financial position if they cannot raise full deposit monies themselves and own any part of the property outright.
High levels of borrowing is part of the reason the mortgage market has got into the mess it has so lenders are tightening up on their criteria to avoid the amount of bad debts which have been accrued previously.
You should not prejudice your position and it is wrong of your son and/or the solicitors if they are pressuring you to do this! Even if you have a private loan agreement in place you are potentially weakening if not destroying your position by writing a letter stating that the money is a gift.
Once the original mortgage is registered on the property the consent of that lender would be needed to register any further legal charge in your favour, without it you could only get an equitable charge registered and it could cause problems if the lender susses that they were lied to in the first place.
If you think about it if you told the lender the truth, would they lend the money? If not then it is essentially mortgage fraud!