Someone told me that the "real reason" was that he was trying to influence the UK government and/or civil service. The various organs of the UK government are all nominally "His Majesty's Something-or-other", so it's a tricky situation if the monarch tries to interfere. However, in practice, the monarch has no real power. The rumour is that he was pushed out by the government due to this interference. I've heard that the current Prince of Wales (Prince Charles), has likewise tried to influence the government, e.g. in favour of homeopaths, etc.
According to the wikipedia article at least, it does seem that there were some political objections to King Edward, but from what I've read and heard, the main reason was the marriage issue. While Edward's political statements and leanings might have made him less popular, without the marriage issue, he would not have been forced to abdicate. He definitely did not take any action (apart from making some political statements) to interfere in the government.