Although it is possible, especially in BrE, for a singular NP functioning as quantifier to a plural NP to govern the verb in the plural, e.g.
A group of demonstrators have entered the building.
(where most AmE speakers would probably prefer 'has entered...'), the converse is not. Thus we cannot, in any variety of English, have e.g.
*Several groups of demonstrators has entered the building.
or, for that matter,
*Many kinds of food was on the table.
And since the number of the verb in a 'there is/are' construction is always the same as it would be in the canonical form of the sentence,
*There was many kinds of food on the table.
is clearly ungrammatical.
The correct version of your sentence is therefore
There were many kinds of food on the table.
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