For a normal tourist the minimum budget would be around 50 EUR per day. That is just basic necessities, like a bed in a hostel dorm, some food from the supermarket, cost of transport to the next city and maybe a cheap activity or sight. For a 6-month trip this works out to about 9 000 EUR. That is without the flight ticket, which is about another 1000 EUR if you are flying in from Australia. You can distract about 20 EUR for every night that you stay for free with friends or family, but still you'll need a ton of money.
For something that I would call a fun trip (= being able to afford some fun things every day) I would bring about 70 EUR per day and person, which works out to 12 600 EUR (24 760 AUD) plus the flight ticket.
Important: You cannot just travel around Europe as you like, as a tourist you are limited to a stay of 90 days within the Schengen area. You either need a special visa (like a Working Holiday Visa for Germany or The Netherlands for example, these are available to Australian citizens) to stay for the 6 months that you have planned or you need to return to London frequently to spend no more than the allowed 90 days in a 180 day period inside Schengen.
http://en.wikipedia.org/wiki/Schengen_Agreement
A cheap way of getting from A to B during winter can be the Eurolines bus pass, check out whether it suits you. (I doubt it, since I assume you have a reason for going to these cities in this particular order.) Still it can be a good way of connecting between big cities. See www.eurolines.com
If you are not a resident of Europe and can afford it, look into getting 2 3-month Eurail global passes or maybe some regional or country passes. See http://www.eurail.com/ and Rick Steves' site (http://www.ricksteves.com/rail/) for more info. Just note that Eurail is not always the bargain it seems to be, you need to compare carefully to the price of regular tickets - and not just regular train tickets, but also to bus, plane and car (rideshare as well as renting).
For cheap flights within Europe see www.skyscanner.net and www.whichbudget.com
Since you seem to have fairly fixed dates, book point-to-point tickets in advance to save money. You can book bus and train tickets up to 3 months in advance.
[ Edit: Edited on Oct 28, 2008, at 2:18 PM by t_maia ]
