I would like to understand how the Cookies Law, will affect the web analytic reporting? Is there another way of tracking?
If the ICO law is ever fully enforced it will cause havoc for UK businesses that are already suffering from several years of atrocious economic conditions. If you want to use web analytics on your site now you'll need to ask people to opt-in first, which very few people will bother to do. You can see the ludicrous opt-in box that the ICO expects UK business owners to place on their site here.
In reality the way Google Analytics performs anonymous aggregate data collection should be the model that others are following, but instead this ignorant law has somehow got through the net without consideration for it's ability to protect users privacy or the impact it will have on any business that utilises the web.
Log file analysis isn't the solution to the problem because the most important metric to analyse is conversions, so you can make changes that increase their frequency; without a persistent tagging mechanism you'll only get a vanity metric reporting the number of conversions you've achieved, but none of the referral or click-stream data required to take any action. In fact, log file analysis is also more problematic from a data protection perspective because many log files contain IP's--which are considered PII--and many small websites aren't actually following the standard UK rules regarding the protection of PII.
I think that it's unlikely that this law will come into full force in its current form; however, it's worrying to note that it's even got this far and potentially could be enforced. If things like this continue it could help factions who want to see the death of the web, where people don't use a browser to access sites, they use an "app" with its own TOS where your consent to tracking is buried within a host of other conditions you never bother to read before installation.
I'm assuming you are referring to the EU cookie law, which requires that all users visiting your site must explicitly opt-in to all non-essential cookies.
As far as I can tell, by the letter of the law cookies from Google Analytics do not fall under "essential" and so you would need users' explicit consent to use Google Analytics. It may be feasible to claim that GA is essential to your site - without it you wouldn't be able to understand what your users need and cannot run a business.
However, I don't think the cookie law is really enforceable and almost no sites have complied with less than 60 days remaining. The ICO cannot police billions of web pages, and will likely only go after the big sites like Facebook or Google if they do. (Heck, huge sites like those may even pay the fines if they make more than the fine from being able to track users and serve targeted advertising.)
If you wanted to track users in another way there is absolutely nothing stopping you using server logs to do mostly the same things GA does (Which is exactly why the law is silly and misguided IMO.)