Q:

Why can stores around Diagon Alley use electricity?

If magic interferes with electricity, shouldn't there be an area around Charing Cross Road where there is no power, or at least really unreliable power? 
I know of course that the real answer is the author wrote it that way. I'm just wondering if anyone had a bit more. 

A:

Magic from Diagon Alley probably doesn't mess with the Muggle technology, for whatever reason.
That's not to say that there wasn't Muggle technology in the vicinity that could have been affected by magic. I think that Möoz is right to query this. But I think that it's inevitable that a busy street in central London would have technology that might be affected by magic. Affected how? Here's the relevant quote from Hermione.

"All those substitutes for magic Muggles use - electricity, and computers and radar, and all those things - they all go haywire around Hogwarts, there's too much magic in the air."
(Goblet of Fire, Chapter 28, The Madness of Mr Crouch).

I looked through the passages in the books which feature Diagon Alley for any hints of people trying to use Muggle technology and couldn't find anything. I think part of the reason for that is that these scenes are so brief (and focused for the most part on people doing magic) and partly because the Harry Potter books were written and set in a time when mobile technology was much less widespread. Nowadays, Muggle-born kids might be trying to get their phones to work in Diagon Alley and we could tell whether magic was getting in the way or not. Alas, we have no such clearcut canonical demonstration.
The Leaky Cauldron is, however, said to be situated next to some large, well-traversed shops.

"This is it," said Hagrid, coming to a halt, "the Leaky Cauldron. It's a famous place."
  It was a tiny, grubby-looking pub. If Hagrid hadn't pointed it out, Harry wouldn't have noticed it was there. The people hurrying by didn't glance at it. Their eyes slid from the big book shop on one side to the record shop on the other as if they couldn't see the Leaky Cauldron at all.
(Philosopher's Stone, Chapter 5, Diagon Alley).

These busy shops, combined with the central location of Charing Cross, point to a bustling Muggle environment. Computers in those stores wouldn't be as commonplace in 1991 as they would today but there still would've been automated tills, managers using computers to do the accounts, and so on. As Anya Mae says, a black hole of malfunctioning Muggle appliances would've been picked up on by the media or the government at some point. Obviously, the Ministry of Magic has a fundamental duty under the International Statute of Secrecy to prevent that sort of suspicious activity being noticed or linked to magic in any way. I think we can conclude that if there had been widespread technological failure around Diagon Alley due to magic that the Muggles would've noticed it. And that we can be equally sure the Ministry of Magic would've prevented any such discovery.
So either: 

Diagon Alley didn't have the same quantity of "magic in the air" as Hogwarts, or
The Ministry must have somehow taken steps to limit the impact of this magic on Muggles.

The first option is possible. Look again at Hermione's statement. It isn't just that magic + technology = chaos. There's an important distinction to be made between magic in the air and "too much" magic in the air. In other words, the quantity of magic matters. Hogwarts has this effect on Muggle technology because of the sheer volume of magic being performed in a confined area. The youth and inexperience of those performing the magic may also be contributing factors. This explains why Hogwarts makes technology go haywire and individual wizarding residences don't.
However, I don't think it's probable that Diagon Alley has less "magic in the air" than Hogwarts. Both locations have a lot of witches and wizards doing magic in a (relatively) confined space. I think that if Hogwarts makes technology go haywire then Diagon Alley would too.
Yet we've concluded that Diagon Alley would not have had this effect on Muggle tech. The only logical explanation, to my mind, is that the Ministry of Magic has taken steps to actively suppress the 'leaking' of magic out of Diagon Alley into the Muggle streets around it. There's no definitive canon proof to back this up. However, it is strongly hinted that there are spells on the Leaky Cauldron which stop Muggles being able to see it.

Harry had the most peculiar feeling that only he and Hagrid could see it.
(Philospher's Stone, Chapter 5, Diagon Alley).

If there are spells which serve to keep Muggles out of Diagon Alley then it's not too much of a stretch to say that there are spells which keep magic (and it's effect on technology) in.

