For those not aware of the situation in the UK, this is how I understand it to be:

Typical holiday provision is 20 days, with 25 increasingly common (most of the jobs I've had offered 25 days). These are paid at full salary. Longer service or contract negoations will often result in more holiday. I've never heard of any company offering reduced holiday to new staff, however it is common that you can't take any time off for the first three month probationary period.

Most companies won't rollover time without special arrangement and will reserve the right to make you take at least part of your holiday when they tell you to and at short notice (ie. if there's not much work on).

There are no personal days/duvet days/etc, just sick days (larger companies might offer personal days, but the're just sick days that you don't have to pretend to be sick for).

A company can't set a limit for the number of sick days you take, but they'll start asking questions if you take too many as it will be affecting their business. Some operate on 'sick events' so if you take a day off, you might as wekk take a full week, as they count consecutive days as one event.

As far as I am aware, there is no obligation for a company to pay you for a sick day, but many do so out of goodwill. If you have more than 5 days off, you can claim benefit (minimum wage) from the state.

There are various laws that protect genuinely sick people from losing their job, but I'm not aware of the details.