The best strategy for the national lottery is not to play. This is especially true after they essentially halved the expected value a couple of years ago which I worked out the maths of here, but it was still very much true before.
However, if you insist, then there is something you can do to increase your expected value. For the smaller prizes like matching 2 or 3 balls you get a set pay out (a free ticket or £10 respectively), but larger prizes are shared between all those that won. That means that it is better to pick numbers that other people didn't pick.
As an illustrative example, on the 30th March 2005 the American Powerball officials noticed something strange going on. While there was only one winner of the jackpot, the second place prize (which you get for matching 5 out of the 6 balls) was shared between 110 different people. There was an investigation because they suspected fraud, given that there were usually about 4 or 5 winners. After interviewing some of the winners they found out that each had received the numbers in a fortune cookie and had been using them thereafter. The manufacturer of the fortune cookies Wonton Food Incorporated had used only a few different combinations of numbers for their cookies and so a lot of people had been using the same ones. This is one of those stories that sounds too good to be true, but it checks out of Snopes.com.
So the only strategy you can possibly have in the lottery is to minimise the amount you will have to share if you do win. This means analysing which numbers other people are going to pick. Given that humans are supicistious (particulary those that play the lottery) that gives us some clues. Do you know what the most common set of numbers is? 1, 2, 3, 4, 5, 6 which has about 10,000 picks. This means that if it does come up then a £3,000,000 jackpot would net each winner about £300.
Other common choices in order of worst to better are the number 7 (the individually most picked number and often just thought of as lucky or sufficiently random), numbers under 12 for months and numbers under 31 for days. The prevalence of dates is very high.
Good picks are 13 (i.e unlucky) and generally numbers above 31. Since the introduction of the numbers 50-59 a couple of years ago those make very good picks because many people stick with their numbers forever and so have remained with their numbers from before.
But, to end this article I think I should remind you that the best strategy is clearly.... well you know what I'm going to say.