3 balls (£10→£25): This prize more than doubles. That's very good. A tenner never feels like a very exciting prize, and people often plough it back into buying more tickets, whereas £25 feels a bit more substantial. If you play the lottery once every Wednesday and Saturday then you ought to win the three balls prize about twice a year. At present that's £20 back on an annual outlay of £100, in the future it'll be £50 back on an annual outlay of £200. 4 balls (£60→£100): This prize doesn't quite double. The extra money Camelot are spending on the three ball prize is being partly taken back here. But this is quite a rare prize to win. If you play twice a week, then you'd only expect to win the four ball prize once every ten years. Meanwhile you'd expect to have won the three ball prize twenty times, which means the four ball payout is really quite miserly. 5 balls (£1500→£1000): This prize actually drops. You'll be paying out twice as much in stake, but your winnings will be only two thirds of what you'd have won before. And this is a much (much) rarer occurrence than three or four balls. Playing twice a week, guessing five balls correct should happen only once in 500 years (ie, during the average lifetime, never). 5 balls + bonus (£100000→£50000): This prize halves. That's a really miserable return, given that guessing five balls and the bonus should happen, on average, only once every twenty-two thousand years. That's roughly how long ago it is since the last Ice Age. £50000's not to be sniffed at, but there are much quicker ways to earn it. 6 balls (£4.2m→£5m): The jackpot rises, but not by much. Camelot could have doubled it, but they've chosen not to, correctly noticing that £5m is life-changing enough so why give £8m. If the very first humans had bought two lottery tickets a week, they might by now have won the jackpot once. Don't get your hopes up.
Come the autumn there'll also be an additional way to win, which'll be called the Lotto Raffle. In every draw 50 people will be picked at random to win £20000 each, which'll be a nice surprise. This is a new innovation, with prizes totalling £1m, which helps to explain why some of the prizes offered for other categories are being reduced. But you're still very (very) unlikely to be picked - in this case only once every 6000 years.
One way to assess the impact of Camelot's new regime is to calculate what would happen if you bought 13983816 tickets. That's every possible combination of balls once, and would (currently) set you back £13983816. Here's how much you'd win.
At current prices you'd have paid £14m for your tickets but you'd only get £8½m back. That's a 60% return, which isn't great.
OK, now let's try the same in the new £2-a-ticket regime. What happens if you buy one of every ticket, but at twice the price?
(up to) 50
In the future you'd have paid £28m for your tickets but you'd only get £14m back. That's a 50% return, which is worse than before.
Camelot's price rejigging sounds like it's in their favour, not yours. But these figures are warped by the jackpot, which is relatively stingier in the £2-a-ticket model. Let's try a more realistic calculation, based over a typical human lifetime.
What would happen if you entered the lottery twice a week every week for 50 years? During that time you'd expect to win 100 three ball prizes, 5 four ball prizes and nothing else. Under the current scheme you'd win £1300, but would have spent £5000 altogether - a return of 26%. Under Camelot's new scheme you'd win £3000, but would have spent £10000 - a return of 30%. So the new scheme's actually slightly better, percentagewise, although you'd have thrown away £7000, so in that respect it's worse.
In conclusion, the doubling of the National Lottery price will mean more chances to win, and a better return for those getting three balls correct. But it'll also suck twice as much money out of your budget, without returning twice as much in prizes. If you can afford to lose £7000 over a lifetime, I say go for it. You never know, you might get lucky... but Camelot will always be luckier.