At one month out, you should consider booking your van. This is important because the longer you leave your bookings, the harder it may be to get an affordable moving company. This also goes for moving, if you're allowing a firm to pack and move you.
Packing firms may also need plenty of warning to be booked, so ensure you investigate this fully before committing to booking them with a month of time. You may need to book them sooner., or may have a little leeway. Booking at one month in advance (or more) also means its easier to collect and decide, impartially on the quotes you collected in the previous weeks. These quotes may have seemed a long way off, but at 30 or so days until you move, it may seem like a long way off, but depending on the size of your house it may be no time at all.
If you're moving house and booking a firm to help you, you may also want to consider booking a cleaning company to come in and clean behind you. They can clean your house, after your belongings are packed and have professional methods for removing stains, marks and other tricky marks on walls, doors and carpets. Even if you're moving yourself, you may need to hire a professional cleaning firm to fulfill your contract with your landlord.
At one month to go you should also start investigating utilities and other things that will transfer with you - moving is a good time to take advantage of any offers that you might get with your phone, electricity, Internet or gas. Taking advantage of this now may not make sense, but in the long run it means you can investigate your options and make an educated decision on your utilities and other billables.