Oh it is very urgent.

A few years ago my boyfriend flew in and we wanted to stay at a B&B. It was..you guessed it...the week of the 4th. It was very hard to get two consecutive nights in the same place. We finally found a place in Plymouth.
It worked out well in the end, we really loved the B&B, and the owners were very friendly.

Again, Good Luck. I hope you find something.