You absolutely can! It's not a public fund.
If you guys qualify, you can also apply for child benefit. Just be sure your husband is the applicant. Basically you guys can apply for most anything you qualify for, just your husband needs to be the applicant and he needs to not be paid MORE because of you. So he can claim as himself and your child, but not anything extra.
When your child turns 3, you'll get the 15 hours of free childcare. What stinks is that you can't get the 30 hours of free childcare even though to qualify, you both have to be working. Will you have ILR by the time your child is 3? If so, you'll be able to get the 30 hours. It's term time only and often doesn't cover a nursery's full cost, but it will save a couple hundred pounds a month if you qualify.