The problem is that the broadband connection is subject to a contract, and contract means that you must have a local bank account - which is very likely unavailable to you if you're unemployed. Even when you open an account you can't apply immediately - at least one provider rejected my inquiry on wording that the account was created less than a month ago (actually, not rejected completely, raised the price twice - but that was even more humiliating).
All that means that even in the best case it can take a month or two before you even can try to apply. And don't believe those terms in the ads, like "only 3 working days" or something - in reality, it took 35 days for our current provider to go a way from the first inquiry to actual connection.
There is no WiMAX in London and if you're not in Wi-Fi hotspot zone and you have no cable, the only solution is 3G network. Again, not all the operators offer pay as you go (prepaid) broadband - for example, last year Vodafone did contracts only with all the consequences explained above. That's not the only problem - the speed is poor, VoIP is fought etc.
By the way the best choice for visitors and people as short-sighted as me is T-Mobile broadband. They offer only 2 Gb of traffic for £15, but doesn't cut you off when you're out of this amount - and that makes the deal unique. After the limit reached, you still can browse and IM (which is most probable enough for mobile usage). In other words, for £15 you receive unlimited browsing for a month, though with some restrictions applied after your first 2 Gb.
After you finally get a cable don't expect surprises to cease. Many providers don't offer unlimited plans which are default option in Moscow - instead, traffic is capped at 60-80 Gb per month and is paid for additionally if exceeded (one of the reasons is that people are supposed to use special "video on demand" services with dedicated hardware and connection).
Also, the traffic is not always but often "analysed" and "prioritized" - which basically means that your different connections face different speed restrictions depending on their type and time of the day. That means that you receive your line speed at any time only for certain types of traffic (like browsing, VoIP) and for other types ("fishy" ones like P2P and FTP) speed is handicapped at the most convenient hours.
Nevertheless, this post is written via our new home broadband. Better late than never.