Time off for dependants will cover it. Its a statutory right for unpaid time off to cover a sudden or unexpected emergency or breakdown in childcare arrangements. It allows reasonable time off to make alternative arrangements for the care.
The legislation doesn't specify a set time as each case will be on its own merits however it states 'usually 1 or 2 days' will be classed as reasonable. Following that an employer would usually look to offer unpaid leave or use holiday or if strict/mean count it as unauthorised time off.
There are no limits on how many occasions of TOFD a person can have. You MUST though follow the company absence reporting, usually make contact asap, notifiy how long you anticipate you will be off for, keep them informed if things change etc (check your company policy). That will comply with your side of the bargain under the legislation.
There was a case where a woman was sacked after 17 different occasions over about 2yrs (can't remember name right now) and she won the case as she had followed all the reporting procedures to the letter and she couldn't have done anymore (her child also had a condition that her employer knew about that made it difficult for her to get other care).
My company allows 2 days then anything after will count as an absence against them (we have a policy that uses occasions of absence for disciplinary stages) but each case has to be considered on its own merits.