Short Connection

I am looking to book a multi city flight to South America through a fare compare site.

Current itinerary:

• London to Lima (6th Feb)
• Lima to Rio (28th Feb)
• Rio to London (6th March)

My problem is that flight 1 goes London - Madrid - Lima with just a 1h 1m layover. However because it is "one flight" through one airline, would I be covered if I missed this flight through a delay on Iberia's behalf? i.e. would Iberia put me on the next flight either next day or whenever?

This is different to other questions as this involves "one flight" of many booked through a travel site. Thanks for you help!

edit: I am not taking any checked in luggage and it looks like Terminal 4 to Terminal 4 transfers recommend 45 mins minimum to transfer at the airport https://www.iberia.com/gb/fly-with-iberia/madrid-airport/connectiontime/