Corkscrew
A couple of wooden spoons/slotted spoon etc to stir and serve
BBQ? Perhaps just a brick stand people can put disposable BBQs onto?
Bins for bathrooms, bedrooms, kitchen
A mix of glasses - wine (one size is fine), flutes, large tumblers, small tumblers
While you only need enough crockery for the occupancy (maybe with 1 extra for guests), enough mugs (and side plates) for twice occupancy would be useful to allow breakfast and lunch or afternoon tea and dinner before needing to washup
Decent sharp knives - bread knife, carving knife, chopper (doesn't need to be massive) and a couple of small ones (and a sharpener!!)
Mixing bowls that can be used for serving as well
1 or 2 ovenproof dishes (for lasagna, oven bakes etc)
Couple of baking trays or baking sheets or roasting tin
(Optional, a pie tin or cake tin or bun tray)
Whisk
Weighing scales and measuring jug, or set of measuring cups and spoons
Teapot and cafetiere
Small jug (does double duty for gravy/sauces) and a water jug (can be useful for making squash etc)
Ice tray in freezer
Some way to put things in fridge - plastic tubs or covers on bowls etc (leftovers, marinading meats, salads to last 2 meals etc)
Sealable storage containers for anything you want to leave there for future visits (flour, pasta, rice, cereal etc) - probably in a lockable cupboard along with a few tins etc for yourselves away from paying visitors
Pillows, duvets, sheets and covers - spares if you have space
Lamps for each room - sitting room, bedrooms etc.
Outdoor items - chairs, table, rug, maybe umbrella/shade
(Possibly picnic type glasses and crockery if you have space and think there will be lots of eating outdoors)
Outdoor lighting of some sort - for safety
Torch
Emergency contacts list - owner, local contact, any maintenance people locally (plumber/electrician etc), and also useful contacts like local taxi, takeaways, dry cleaners/launderette, tourist office, …
Pack of cards
Books and DVDs etc, board games
(Maybe a few toys for small kids, if in good condition and your DCs have things they've grown out of that you can use - blocks, cars, a doll, books for DCs etc)
Cleaning items -
washup brush (clean pot scrub for each letting), tea and hand towels for kitchen, bathroom towels, beach towels if you want,
washup liquid, spray cleaner, window cleaner spray
Sweeping brush, dustpan and small brush, tools for any fire/stove or BBQ, hoover, mop and bucket, basin, basket for laundry (if you have washing machine), clothes horse, clothes line (outdoors) and pegs (need a way to dry clothes even if you don't have a washing machine),
Rugs/throws and cushions
Decorative items on walls
Protective covers for any tables etc - 2/3 trivets, placemats, etc
Oven gloves, apron
Useful consumables -
Salt and pepper
Cooking oil
Teabags and ground coffee
Sugar
Cleaning items (see above)
Tin foil, cling film, greaseproof paper etc
1 roll kitchen towel
2 or 4 pack toilet roll as well as a full roll on holder in each bathroom
Small bottle washup liquid
Handful of dishwasher tablets (if dishwasher)
Small pack powder or small bottle liquid or handful capsules of laundry detergent
Box matches