One thing that sometimes gets forgotten in the war on reshes is that they are great shelter for sheep and especially lambs.
Which said, the most effective way to reduce them is to top and then weed-wipe the new growth - the poison is absorbed much more readily through the softer, new growth.
If you don't want to, or can't (due environmental scheme for instance) use chemicals, then topping in early summer (after the ground nesting birds have fledged and left) and again 6-8 weeks later is also fairly effective.
If you like providing habitat for ground-nesting birds, then don't top all of it every year, but rather top different thirds each year to give a range of heights and some open areas.
Oh, and native ponies will probably do a reasonably good job too, over time.
As everyone else has said, probably too late to do much about it this year as the ground is likely to be very wet by now.