We don't have an Independence day in the UK.
We do have a burn-a-guy-on-a-bonfire day though
That's probably our closest example but it isn't till November. And it isn't a national holiday either.
*smiles innocently*
We're nice gentle people in the UK.
The four countries of the UK also each have saint days from way back in the past, but while sometimes I think these are national holidays, in England St George's Day (23rd April) is not. Well, the UK is a bit complicated that way.
@Loa - I'm sure she loves all you guys too xD. Probably more than she does us right now, as parliament interrupted her day out to Royal Ascot by delaying her speech to open parliament and she did not look overly amused with having to give it...