Have a look at Vodafone. (vodafone.co.uk) They have a "passport" pay as you go plan that you can add internet to at GBP2 per day. (The data allowance is not great though.)
There may be better deals out there but that is what I use.
I just used this throughout Europe. Works great. 25mb per day for a lot of countries, 5mb per day in others (including Sweden).
Was infinitely useful, including being able to 'online checkin' for a flight that had 0 people in the bag drop queue, and a million in the normal queue. Saved me 35 minutes of queueing at BRU
And see this thread:
Communication & Internet (which specifically discusses many pre-paid SIM options all over the world). In addition,
PrePaidGSM.net is a good forum.
I just tried to get the link from the Vodafone UK site for the countries, but they are doing maintenance so their site is down.
France, Germany, Netherlands and Belgium were all included in the 25mb. If you register for Vodafone "freebees" you also get 500mb to use per 10GBP charge you make, in the UK. I can't recall the other countries, as these (and Sweden) were the only places I were going (and for those who know where I work, this is a cheaper way of using data, although calls were not wonderful; I don't make calls on my Vodafone SIM, I use my companies SIM card for that

).
*edit*
Vodafone UK site back up, List of countries with 5mb and 25mb limits for the 2GBP a day on pay-as-you-go:
http://www.vodafone.co.uk/Lightbox/VFTST061981
It's a popup window taken from
http://www.vodafone.co.uk/personal/...ng-abroad/using-the-internet-abroad/index.htm in the following section:
Pay as you go
As a pay as you go customer you’ll automatically benefit from Vodafone Data Traveller and pay just £2 a day (midnight to midnight, UK time) for each day you use it.
Vodafone Data Traveller countries (these may change from time to time)
One thing to keep in mind is it's *per country per day*. If you change countries during this time and keep using data, you'll be slugged another £2 from your balance.
In addition, it's not possible to use an AU credit card to top-up your account online or via phone. I bought my pre-paid vouchers via eBay (reputable seller) and it was less than £10 for £10 of credit (was around £8.50) with topup codes just emailed to me. Don't forget to setup your Freebees online though first.
Vodafone will also ship you up to 2 free SIM cards, but you need to have them sent to a UK Address (I had mine sent to the office and forwarded to me, so that's probably a hurdle for most people).