Toilet Cistern not filling

[BackforGood]

Toilet is on 2nd floor, fitted as part of new bathroom about 10 yrs ago. Not a sani-flow or anything.
Over time, (some months) the gap between the flush, and the cistern filling back up again has got longer. Started as a 10 second or so delay, and now can be up to 5 mins.
When it fills, it doesn't trickle in or anything, it all fills quickly / at normal pace, just not until 5 mins or so after the flush.

Any idea what this might be?
Or even, if it is anything I should be worried about ?

TIA

take the lid off and photograph what's inside, please

On the supply pipe, can you see one of these, where the slot in what looks like a screw-head is actually a shutoff valve?

www.screwfix.com/p/isolating-valve-15mm-10-pack/32802

Thank you PigletJohn. sorry, I got called away and was then out last night.

Yes, it has one of those that you have linked to.

I can't work out how to get the top off the cistern though. Unlike my (older model) toilet downstairs, this cistern lid seems to be fixed, and I can't see any obvious looking screw or anything I can undo to look inside.
It says Twyford on it but I can't see anything like a model number. Looks similar to this

oh, you have one with a button in the lid

see if the ring round the button will turn to unscrew, or if, when you press the buttons, small screws are visible

The slot on the valve I linked will turn the water off when the slot lies across the pipe; and on when parallel to the pipe. Which way does it lie now?