I came across MacNeice because this book is at the program of an ultra-competitive set of exams to become an ESL teacher in French high schools. And you wonder why, save for the fact that maybe they wanted someone to conveniently represent at once both Irish literature and poetry, and whose poems are not too long to analyze in an exam setting.
The overall feeling when reading The Burning Perch is of superficial brilliance and not much else. MacNeice is a deft hand with the technicalities of verse and a virtuoso when it comes to dazzling the reader with the breadth of his vocabulary and cultural references (the Bible! the Classics! all the trips one can take on the Grand Tour!), cleverly mixing them with the conveniences of modern life or with nursery rhymes. Beyond that, running themes are such lofty clichés as death, remembrance and childhood, and typical 20th century fears about technology.
Unfortunately, it often seems that his overuse of exotic names, cultural references and the likes serves to obscure the lack of depth in most of the poems. It's hard to find a memorable line and some poems look like fillers in an overall slim collection (Château Jackson, October In Bloomsbury, Flower Show).
The book was posthumously published in 1963. Thinking about poetry published that year (Adrienne Rich, Sylvia Plath, Anne Sexton, Allen Ginsberg) or even about William Carlos Williams who also died in 1963, MacNeice's poems appear hopelessly dated and irrelevant, mentions about computers and vacuum cleaners notwithstanding.
When reading about MacNeice's life, one gets the sense that he was chummy with much better poets than him (Auden, Eliot, Spenser) thanks to his typical upper crust education (public school, Oxford) and it's because of these connections he was propelled to the enviable status of (minor) published poet.
Apparently his masterpiece is Autumn Journal, so should you be inclined to reading his poetry anyway, maybe this is where you should start.