It might be a bit further than an hour (about 1hr 30 min), but the very best place to hear them is Paxton Pits, at Little Paxton, which is just off the A1 at St Neots. It's well worth the journey, as there's around 20-25 singing males in a fairly small area. This is the highest concentration in the country, so you're totally guaranteed to hear them. Pick a fairly mild still evening - after 6pm is best, but it doesn't have to be dark. They sing all day, but especially in the early mornings and evening.
Check their website
http://www.paxton-pits.org.uk/nightingale.htm and browse around for directions etc.