...there is a satellite dish on the front with cables to the kitchen and the living room.
The cables are twin-cables (joined together) and each one has a metal screw cap on the end.
What are these called and will they fit my telly?
...my old setup was a dish with a DIN cable stuck into to Freeview box (TV didn't have a DIN socket) which was then connected (HDMI I think...? ) to the TV.
The new telly obviously has built in Freeview so I don't need the box... but I dunno what those twin metal connectors do (or how to connect my telly to them if it hasn't got twin-metal nozzles to receive them).
How's it all work?
I'm confused by 'twin cables, joined together'. If you remove the metal caps, is the cable beneath coax (co-axial)? ie, beneath the outer plastic casing, does it look like aerial cable with copper mesh/foil round the outside and a central solid copper core? And have you traced these cables back, do they go all the way back to the Dish, continuously? If the answer to these questions is 'yes' then I think they should be good to go, straight into a satellite receiver.
Re: your previous installation, if you had a Dish feeding into a box, it wouldn't have been Freeview, it would've been Freesat
(same kind of thing, but for satellite rather than aerial).
Finally, regarding your new telly, check whether it has in-built Freeview of Freesat (some even have both). Unless it has Freesat, you'll need a standalone Freesat receiver and then link that to your telly with an HDMI cable.
Or if the telly's Freeview and already ordered and can't be changed, you could always put up an aerial, provided you have a Freeview signal where the house is.