I recently got an Icom ID-51E PLUS2 and its smallest tuning step is 5kHz. I looked at the list of repeaters in the UK and many are between 5kHz stops, such as 145.6125MHz. Is this expected? Do you just tune as close as possible to it or am I missing something regarding repeater operations?
While it is true that you have a 5 kHz tuning step, you do also have a 6.25 kHz and a 12.5 kHz tuning step. These should enable you to tune to the desired frequency.
Open the quick menu screen. Push D-Pad up/down to select the tuning step. Then press D-Pad Enter to lock in that tuning step.
If that radio model is actually as you describe (I'm not familiar), then you cannot use it with that repeater. A 2.5 kHz frequency error is sufficient to make (5 kHz deviation) FM unusable.
If you can program the radio with the specified frequency, as opposed to using VFO controls, that may work. Even if it only accepts 3 digits after the MHz decimal point (so that you must enter 145.612 or 145.613) then that will be a 0.5 kHz error which I would expect to be workable if not great.