Can you claim child care expenses on your tax return in the UK?
No, you can't. However, there is a tax efficient way of getting childcare that is available through some employers: childcare vouchers
In brief, if your employer chooses to offer these, then you can get up to £243 per month of "vouchers" that you can then spend on eligible childcare providers - basically anything like a childminder, nursery or nanny, but not normally your own relatives.
Normally employers won't provide them for free, but instead provide them in exchange for a "salary sacrifice" which is from your gross salary - so roughly equivalent to getting a tax deduction. Both parties (employer and employee) also save on national insurance contributions, which creates a significant incentive for the employer to offer the scheme. Most large employers do offer it.
Note that the limit of £243/month is a total for the parent, not per child.
The UK government has announced that the scheme will be changed from April 2011, so that people who start getting the vouchers from that date will only be able to avoid basic rate tax (20%), so those paying the higher marginal rates of tax (40%, or 50% for very high earners) will still have to pay the difference between their marginal rate and basic rate on the vouchers.