The link below mentions "special licenses" and is a general interesting description of how to get married in Georgian England.

The reference below states: "Because of the expense, marriage by special license was reserved for the very wealthy and well connected." Notice that there is no special limit requiring the couple be peers in this source.

The general implication of all the sources I found is that there was no time limitation in obtaining a special license. You simply went to the Archbishop of Canterbury and bought one with no waiting period. However, as mentioned by various sources the Archbishop was not required to issue the license and could be selective as to who was allowed to purchase one. The primary variation was the issue of who was eligible to obtain one.