Sorry but Kings Cross left luggage facility doesn't open on Sundays. It's only open (from 0700 to 2300) Monday to Saturday.
However St Pancras station is just across the road from Kings Cross (which is why they share a common Tube station) and has left luggage facilities open from 0700 to 2200 on Sundays.
http://www.left-baggage.co.uk/index/locations
Grandad G should ensure that everything is put into a single bag as left luggage is charged on a 'per item' basis (and, at £11 per item per day, it's not cheap!).
Should you still need a direct phone number for the Travelodge, it's 0871 984 6256.