I found this.
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Anyone may apply for discretionary excusal. They should write the details on their summons reply in section 3 question C. A jury officer at the Jury Central Summoning Bureau will make a decision whether that person can be excused based on the details given. If a juror is refused excusal they have the right of appeal against this. The juror should put their reasons for appeal in writing addressed to the Head of the Bureau.
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Fees to carers or child-minders
You may claim for payments you make to a carer or child-minder solely because of jury service. You must provide a receipt, or a letter signed by the carer, to say how much you paid them for each day.
http://www.cjsonline.gov.uk/index.html
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Find out how much it would cost to pay for private carers or respite (to cover) and ask if they'd be willing to pay that expense.
(Should carers be exempt? The jury should be as representative as possible of the population at large, so perhaps if carers were exempt it would be skewed.)