I agree with @Anarchist, it’s highly unlikely a photo would be accepted. Monzo cannot clear cheque by image alone right now, which leads to me believe they’d need the physical thing.
I doubt Royal Mail would pay a claim for a cheque, as the cheque is technically worthless - it’s just an instruction for a bank to make a transfer. The transfer is valuable, but as that hasn’t happened technically no money would be “lost”.
I’m afraid sending the cheques by special delivery or tracked is your best bet. You may find it worthwhile to have the peace of mind opening a secondary bank account just for the purposes of paying in cheques. It’s something you have to weigh up yourself though, because as @Anarchist says, you could always ask for a second copy of the cheque and tell the sender it was lost in the event they go missing.
I guess I was questioning the purpose behind the instruction to take a photo. If it’s as proof for RoyalMail, then fine … but if they wouldn’t pay out anyway … then very strange!
I spoke to my wife, and she’s keen to just approach people and say “Hey we don’t have a joint account just yet … could you re-issue the cheque please?” … I find it a little rude to have to ask though.
An option would be to buy consequential loss insurance, depending on the value of the cheques and how much royal mail will charge, that should cover the value of a cheque if they won’t pay out normally.
If you’ve got a legacy bank account pay the cheques in using a paying in book at a branch or via the post office then when cleared transfer the funds to your Monzo account