Yes, AB. ChuckFickens is, I’m afraid, completely mistaken.
Although magistrates (and of course judges) have the power to disqualify from driving anybody convicted of any offence (not necessarily driving offences) they would normally have to be satisfied that the offence was linked to driving a motor vehicle. For example, a person convicted of a series of burglaries who can be shown to have used a motor vehicle to effect his escapes may face a ban. However to ban somebody convicted of being drunk in charge of a cycle (or a horse or a child) is stretching that principle too far and such a penalty would almost certainly not be imposed (or if it were, an appeal would almost certainly succeed).
Riding a cycle does not require a license and there is no provision to link an offence of drunk in charge of a cycle with a driving licence needed to drive a motor vehicle as CF suggests. There is also no provision to ban a person from riding a bicycle. The excess alcohol legislation (Section 5 of the Road Traffic Act) applies specifically to motor vehicles:
Driving or being in charge of a motor vehicle with alcohol concentration above prescribed limit.
(1) If a person—
(a) drives or attempts to drive a motor vehicle on a road or other public place, or
(b) is in charge of a motor vehicle on a road or other public place,
after consuming so much alcohol that the proportion of it in his breath, blood or urine exceeds the prescribed limit he is guilty of an offence.
This could not be applied to a cycle rider. As I said earlier, there is no power to compel a cyclist to take a breath test at the roadside and all the accompanying procedures (further breath tests, blood tests, urine tests etc.) are not applicable.
In short, as AB has said, a maximum fine of £1,000, though in reality far less than that and I imagine (though have not checked) that this is an