What does the “a’ ” in “a’blowing” signify？

Quotation from A History of the Cries of London: Ancient and Modern

Oh, dearly do I love “Old Cries,”
 Your “Lilies all a’blowing!”
Your blossoms blue, still wet wih dew,
 “Sweet Violets all a’growing!”

Solution 1:

Entries in the OED suggest that in both words the a- prefix is derived ultimately from the preposition on, which is used, as in your examples, before the -ing forms of verbs to give the sense of ‘engaged in’. The OED has, for example, this citation from 1883:

Now let us run out and look at the flowers and the trees all agrowing and ablowing.

One of the meanings of blow, which it clearly has here, is ‘to burst into flower; to blossom, bloom’.

The OED’s earliest record of agrowing is dated 1605. Ablowing is found in Old English, but with the medical sense of ‘swelling’ or ‘distension’.

Solution 2:

Wikipedia says the a- prefix is used to form a predicative adjective with progressive aspect.

OED gives a dozen or more origins/meanings for the a- prefix, but I must admit I can't see any there that really correspond to OP's examples except #11, where it says the force of the prefix is so little apparent, that the derivatives in a- hardly differ in sense (in respect of, say, rise/arise, wake/awake).

So I think in OP's particular examples, the a- prefix either means nothing at all (effectively OED's take), or it can be seen as replicating/emphasising the progressive aspect of the verb (which is also being done by the -ing "suffix" anyway).

The apostrophe in OP's case is arbitrary (you could replace it with a hyphen, or nothing at all).