It may be that the float is catching on the side of the cistern. If so:
1. Flush, stop refill and turn off water.
2. Sponge / vacuum out remaining water from cistern.
3. Slacken nut connecting inlet pipe to base of threaded shank to inlet valve (underneath cistern, slacken no more than one turn).
4. Slacken nut (almost certainly white plastic) holding inlet valve to cistern. (Called a back nut)
5. Rotate inlet valve to ensure float clears sides of cistern.
6. Re-tighten back nut, making sure inlet valve doesn't turn as you do it.
7. Re-tighten nut connecting inlet pipe to shank. As long as you only slackened it one turn, you should get away without replacing the 1/2" internal fibre washer which seals the connection. (Flexible pipes generally don't have these). Make sure valve doesn't turn as you tighten.
8. Turn on water, check for leaks as it fills and correct as necessary.
If you can't get the float free by rotating it, you may need to fit a more slim-line model.
Less likely, but possible, diaphragm washer (seal) under the black plastic cap (top right of picture has gone hard.
Your valve looks like a Fluidmaster 400a fill valve, which would require a 242 replacement seal , but I can't be absolutely sure.
Pretty much whatever make it is, to replace seal:
1. Isolate water supply.
2. Remove cap and washer (Fluidmaster instructions available online).
3. Briefly turn water on with cup over inlet to catch water (flushes out debris). Turn water off again quickly.
4. Fit new seal.
5. Re-fit cap.
6. Turn water on.