This link answers that question: http://blogs.transparent.com/italian/tavolo-or-tavola/
In English, 'too much' is used for an uncountable amount, such as 'too much milk' or 'too much anger'. If you are talking about something of which there is a certain number, something you can count, you use 'too many', as in 'too many cars' or 'too many places at the table'. :)
My understanding is that tavolo is a piece of furniture, and tavola is a place the family gathers to eat together. It's kind of nuanced -- with tavolo being less personal than tavola. So far this understanding has served me well in maintaining my hearts, though I'm open to correction.
In UK English we say 'at table' if we refer to places for diners set at a dining table. We would say 'on the table' or 'by the table' if we are referring to objects placed on or around the table. Only occasionally would we say 'at the table', in circumstances such as 'there is a man standing at the table', but even then it would be better to say 'by the table'. In this instance we are clearly talking about place settings, so 'at table' is correct.
Not a class thing - its received English, or BBC English. As another contributor has already said, its the classic form in English, and found in Jane Austen, etc. You may be thinking of the the Yorkshire dialect where 'the' is implied but not fully spoken (such as literally at ' table) with a gluttoral stop replacing the 'the', but I don't think this is being so subtle. 'At table' is good Oxford English. The question "Are you at table', for example, means 'have you sat down to eat?.