The match can’t be a friction match as these were not invented until 1826, long after the publication of ‘The Female Vagrant’ in the first edition of Lyrical Ballads, 1798. Instead, the blue flame indicates that it is a sulphur match.
Before sulphur matches, the way to light an oil lamp (if you didn’t have a fire already burning) was to use flint and steel to make sparks to ignite tinder, blow on the tinder until it burst into flame, use the burning tinder to light a wax taper or paper spill, and use the taper to light the lamp. Persuading the tinder to burn hot enough to light the taper was a delicate and time-consuming process, and sulphur matches (which caught fire at a lower temperature) sped up this step.
Even with sulphur matches, the process was tiresome:
When I was young [in the 1790s], the process of obtaining fire, in every house in England, with few exceptions, was as rude, as laborious, and as uncertain, as the effort of the Indian to produce a flame by the friction of two dry sticks.
The night-lamp and the rushlight were for the comparatively luxurious. In the bedrooms of the cottager, the artisan, and the small tradesman, the infant at its mother’s side too often awoke, like Milton’s Nightingale, ‘darkling,’ but that nocturnal note was something different from ‘harmonious numbers.’ The mother was soon on her feet; the friendly tinder-box was duly sought. Click, click, click; not a spark tells upon the sullen blackness. More rapidly does the flint ply the sympathetic steel. The room is bright with the radiant shower. But the child, familar enough with the operation, is impatient at its tediousness, and shouts till the mother is frantic. At length one lucky spark does its office—the tinder is alight. Now for the match. It will not burn. A gentle breath is wafted into the murky box; the face that leans over the tinder is in a glow. Another match, and another, and another. They are all damp. The toil-worn father ‘swears a prayer or two;’ the baby is inexorable; and the misery is only ended when the good man has gone to the street door, and after long shivering, has obtained a light from the watchman.
Charles Knight (1859). Once Upon a Time, London: John Murray, p. 501.
This process was improved by the discovery of chemical ignition in the 18th century:
[Sulphur matches] continued in use throughout the 18th century, but after about 1780 phosphorus devices in various forms began to replace them. For instance, the ‘philosophical bottles’ were small vessels containing a partially oxidised yellow phosphorus and kept tightly corked; when a light was wanted a sulphur match was pushed in, turned round and quickly drawn out, igniting on contact with the air.
Joseph Needham (1962). Science and Civilisation in China, Volume 4 Part 1: Physics, Cambridge University Press, p. 71.
These bottles probably arrived too late, or too expensively, for the characters in Wordsworth’s poem:
The first chemical light-producer was a complex and ornamental casket, sold at a guinea. In a year or so there were pretty portable cases of a phial and matches, which enthusiastic young housekeepers regarded as the cheapest of all treasures at five shillings. By-and-by the light-box was sold as low as a shilling. The fire revolution was slowly approaching.
Knight, p. 502