Ignoring the "London is a World Class City and is better than __________" argument, there are several reasons why an NFL team based in London is a terrible idea:
1) Taxes. This has been mentioned in the thread. Professional athletes have to pay taxes in every state they play in. Don't know how taxes are in London, but not only would they have to pay taxes and convert them into pounds, they would have to oblige by another set of tax guidelines.
2) Bye weeks. Any team going to London for a game would immediately have to have a bye to make up for two overseas flights, which would throw off scheduling. An NFL team in London would have a competitive disadvantage over the road team because the road team would be losing a minimum of 5 hours due to the time difference. That's not taking into consideration the potential toll it could take on an athlete.
3) Not only would you have to relocate players and coaches to London, but you'd also have to relocate Front Office staff (Marketing, Communications, Medical, etc.) and possibly their families to a foreign country for a significant amount of time. The lower level positions (ticket sales, merchandise stores, food vendors, etc.) are easy to fill locally, but higher up position would require a lot more travel than a team in the States.
4) With one dollar being 0.63 Pounds, a London team would have to receive a larger salary cap in order to attract free agents. 31 other teams would be pissed off that the London team would have more money to spend.