This happened on Grace Road in Leicester, UK.
The driver was offered an educational course as an alternative to prosecution, which they have taken and completed.
I believe rule 163 of the Highway Code applies here: (abridged)
Give motorcyclists, cyclists and horse riders and horse drawn vehicles at least as much room as you would when overtaking a car (see Rules 211 to 215).
As a guide:
• leave at least 1.5 metres when overtaking cyclists at speeds of up to 30mph, and give them more space when overtaking at higher speeds
• you should wait behind the motorcyclist, cyclist, horse rider, horse drawn vehicle or pedestrian and not overtake if it is unsafe or not possible to meet these clearances
Leicester UK
Grace Road
close pass
Careless and inconsiderate driving
cycling
cyclist
1.5m