Eric I don't doubt for one minute that the King had considerable support from ordinary people. There are numerous letters in the Windsor Archives and the PRO from people about it expressing their support and most people had had quite enough of Baldwin and his ageing government. But those letters and records are not a majority. Public opinion had had little time to form given that the British Press had censored any mention of Mrs Simpson until the Bishop of Bradford's "recall to religion" speech (widely misinterpreted as an attack on Edward VIII's relationship with Wallis) and that the subsequent crisis lasted such a short time in the public spotlight. It is therefore difficult to get an accurate portrayal of public opinion.
On the other hand we also have the "number" of unpleasant letters that the Duchess of Gloucester received after she and the Duke met the Windsor's in France in 1938 (another attempt to test public opinion).
It is also worth bearing in mind that for twenty years the British public (and the greater public in the dominions) had been treated to newspaper and newsreel reports that were glowing in their flattery of the Prince of Wales and glossed over everything that showed him in a rather less flattering way (which is why so many of his own and his father's courtiers didn't think much of him). His fondness for other men's wives (Freda Dudley Ward and Thelma Furness spring to mind) his pleasure in Cafe Society and his rather low boredom threshold (which for a future King Emperor was a problem - given that the role largely embraces a life of ritual boredom) had all made his parents, the court and significant sections of the government doubt his sincerity and his understanding of the constitutional role he was expected to fill.
On a personal note when we were doing this at school (more years than i care to remember) our teacher asked us to visit our elderly relatives who'd lived through the thirties and ask them about a variety of topics from the depression, to appeasement, to the abdication and the outbreak of war. My grandmother and her sisters who in the thirties were young women living in Yorkshire were still 50 years later utterly opposed to the idea that their King should marry a divorcee - true we found a more diverse range of opinions when we visited a local Old People's home. I suspect that opinion was far more divided than official records allow.
I have little doubt that quite a number of politicians were glad to see the back of Edward VIII - the released records of Baldiwn's conversations with the King do suggest that Baldwin pushed him into a position where Edward was forced to tell the prime minister he intended to marry Mrs S, when she were free, therefore obliging him to accept his Government's advice on the matter. However it is also clear that Edward up to the last was prepared to use unconstitutional methods to get his own way on the matter - there was a lack of trust on both sides which were hampered by Baldwin's rigid view (backed by his cabinet) that the public wouldn't accept a "Queen with two living husbands" and Edward's view "that his private life was his private life". The Cabinet and Baldwin's attitude had been hardened by the way in which Edward behaved in his official duties following his father's death - his late hours, his obvious boredom on official occassions, his preferrences for certain foreign dignitaries over others, his dictats about foreign policy, the way he treated his staff, the way he'd treated his father's servants etc - all of that to a certain extent undermined and weakened his position as king when it came to the issue of marrying Mrs Simpson.
Was it a tragedy that he was forced to abdicate - we'll never really know what kind of King he would have made or what kind of Queen, Wallis would have made - no children though which would have made his reign almost pointless - his brother might have lived long enough to succeed him without the pressures of the Second World War which encouraged him to smoke and drink more either way his eventual heir would have been the present Queen. He had many strong points as did she - neither of them were particularly intellectual though and Edward like the rest of his family could suffer from extreme prejudices. One problem would have been the area of foreign policy in the lead up to the Second World War, he'd received a dressing down from his father over interferring in politics by giving a speech saying the Germans should be "our friends" a few years earlier, though I don't share the idea that either of them were particularly pro-nazi though he was pro-german. (dating to his visit to Germany in 1913 and like many of his generation a determination to avoid a repeat of the carnage of the 1st World War.) We might have had less pomp and circumstance a bit less of the archaic traditions of his father's court, but we'd have had a few redecorations of the Royal Palaces and a more Cafe Society circle than the Aristocratic Country House style of court that George VI and Queen Elizabeth created for themselves.