Learn English – Will the word ‘proportion’ take ‘has’ or ‘have’ for singular

Yes, change to 'have' because it is a plural number of people that have received a blanket. I would change 'small amount' of people to 'small number' of people.

The following extract from Dictionary.com suggests that both the singular and the plural verb form are correct after "none". Usage depends on the emphasis that you want to give to "none" as either a singular or a plural subject. Also evidence from Ngram shows both usages are common.

• None means ‘not one’ or ‘not any’ and it may take either a singular or plural verb.

• Writers are more or less free to decide which meaning is appropriate in their context. This grammatical construction, which is based on sense rather than form, is called notional agreement or notional concord, and is very common.

• So, consider none as singular when you want to emphasize a single entity in a group, but consider none to be plural when you want to emphasize more than one.

Examples are:

• None of the books is/are worth reading. / None of us is/are going to the banquet. However, when none means ‘no amount’ or ‘no part’, it must be singular:None of the debris has been cleared away. / None of the forest is deciduous. So, if your meaning is ‘none of them’, treat the word as plural; if it is ‘none of it’, treat it as singular.

Similarly any of can take both constructions according to the meaning conveyed:

• When used as a pronoun, "any" can take either a singular or plural verb, depending on how it is construed: Any of these books is suitable (that is, any one). But are any (that is, some) of them available?