In answering this question, much depends on how one chooses to define "romantic" and "anti-romantic."
For example, if one chooses to define "romantic" as implying optimism, naivete, celebration of love, celebration of the beauties of nature, and celebration of lofty, transcendent human potential, then it seems safe to categorize Larkin as an "anti-romantic" poet. His verse is often realistic, hard-headed, sometimes even cynical, and deliberately unsentimental. It is not by coincidence that Thomas Hardy, with his bleak vision of life, was one of Larkin's favorite English poets. Yet part of what gives Larkin's poetry its peculiar power is that he can often see and appreciate the beauties of life, even if he considers them inevitably mutable.
In the standard anthology piece "MCMXIV," which describes the eagerness of men to enlist in 1914 in World War I, the speaker concludes,
Never such innocence,
Never before or since, . . .
. . . .
Never such innocence again. (25-26, 32)
Here the speaker clearly asserts that such innocence is a thing of the past, but he also seems on one level to admire the innocence whose passing he describes.
Likewise, in "Talking in Bed," the speaker begins by claiming that
Talking in bed ought to be easiest,
Lying together there goes back so far,
An emblem of two people being honest. (1-3)
Yet as soon as one reaches the word "ought," one realizes that the speaker is describing an ideal that no longer prevails, at least in his own life, if it ever did. Indeed, the conclusion of the poem is decidedly unsentimental. In the intimate relationship he describes,
It becomes still more difficult to find
Words at once true and kind,
Or not untrue and not unkind. (10-12)
A stereotypically "romantic" poet might have closed with a solution to this kind of "isolation" (9), but Larkin rejects such a sentimental ending. Even so, the closing lines show that the speaker does value truth and kindness, however difficult it may be to find words to express such ideals.
"The Explosion" seems, in some ways, a thoroughly anti-romantic poem, especially since it describes the devastating loss of life of miners in an explosion in the pit. The speaker reports, without comment, the conventionally comforting words of a clergyman preaching at a funeral service:
The dead go on before us, they
Are sitting in God's house in comfort,
We shall see them face to face -- (16-18)
A romantic or sentimental poet might have tried to convince us of the truth of this assertion. Larkin does not. He simply lets the assertion speak for itself, allowing readers to decide whether it is genuinely comforting or merely a collection of predictable cliches. Neverthelss, the poem does end on a very tender note. One of the miners, before work had begun, had discovered "a nest of lark's eggs" and had shown the eggs to his comrades (8-9). As the poem concludes, the speaker describes how the widows of the miners, after hearing the sermon, imagine seeing their dead husbands again,
. . . walking
Somehow from the sun towards them,
One showing the eggs unbroken.
Thus, although Larkin is often thought of as a plain-spoken, sometimes even slightly crude writer (his poem "Sad Steps" begins with the memorable line "Groping back to bed after a piss"), there is often real tenderness, real feeling in his poems. Larkin could appreciate love and beauty very deeply; he simply never assumed that they would last forever.