That's just a technicality, I assume to make it comply with other laws about using company money to buy personal items. Payments are deducted from your pre-tax earnings each month, so the saving come from paying less income tax; you can't give the company a wad of cash up-front, or have it all come out of one month's salary.

> you hope that your employer will give the bike to you at the end of that period

They will always give you the bike: Cycle to Work schemes are offered as an employee benefit, the company doesn't want the bike. More important is what happens if you leave the company before that period; e.g. when a previous employer folded I had some some balance remaining to pay (around £500), which was deducted from my redundancy payment.

> The problems are that your employer might not want the extra hassle involved of potentially owning unwanted bikes (my employer has no interest in the scheme)

That's certainly true, and probably the main reason to avoid it (as an employer). Still, it's not much different to having surplus office furniture; at the higher-end, I imagine it's similar to an employee requiring some specialist desk chair, which the company can sell off afterwards.

> he last time that I checked, the tax break was on only the first £1000.

It varies per employer, e.g. I got one up to £1500. More annoying is that it must cover the full price: e.g. you can't pay £100 cash to get a £1600 ebike (although some sellers may fiddle the price tag to get around this!)

The only time I used cycle-to-work was many years ago, so I might have misremembered. However, I've heard that current schemes tend to just give out vouchers that can be used in certain bike shops (e.g. Halfords) on bikes and bike accessories and can be used in part payment for bikes. To be honest, increasing the price limit only really helps people who already committed cyclists, so maybe it's at a fair level.