For mid-price accomodation, try Premier Inn. They are to be found in most places in Gt. Britain, although mainly around major population centres.
They generally cost around £60 per night, plus a fiver for breakfast, but then there's always McDonalds for Brekkies, or a local caff. I've stayed in them in North London (Kenton) near the very pretty Harrow-on-the-Hill, of Harrow School fame and in Caernarfon in N. Wales, both good locations. Kenton being a 15 minute tube ride into the West End (Piccadilly, Oxford St., Houses of Parliament, Imperial War Museum etc.) and the one in Caernarfon right on the Menai Strait and just a few hundred yards from the Castle. Both £60 per night. The other good thing about that chain is that, although often a bit characterless, they are always clean with 24hr. Reception and are safe.
Another idea in the Summer recess, is the Universities. Most will rent out rooms with, if not en-suite facilities, then certainly shared by at the most a little cluster of about 4 rooms. My parents have stayed in them at London and Cambridge Unis.
If you can get a good idea as to where you want to go, then why not try and see if you can get good, possibly student rates, on the trains by booking ahead, preferrably before you leave Oz.
I know £60 X 30 is a lot of dosh, you could combine a week at London Uni Halls of Residence with some odd nights in hotels. The Peremier Inn at Manchester Airport is doing rooms for £45 per night and its only 18 months old, plus there's a pub/restaurant nearby, The Romper where some of us meet one Sunday a month and a 5 minute bus ride will put you at the Airport Rail Station where you can get trains to wherever you want.
You could even start at Manchester, one of my colleagues goes to Oz every year to stay with his ex-wife and her husband - don't ask - and he always flies Singapore Airlines to Singapore, ooh what a surprise, and from there to Perth. Or alternatively end there with a few days in the North West.
A month is a long time and pretty expensive in most countries, but then I suppose you could always try and see if you could get some accomodation from members on here. Any offers?