Similes are a type of metaphor, easily identified by "like" or "as". Check out the reference link below to read about why similes are used in poems.
and he peered out of the great, green-leather armchair by his friend the boss's desk as a baby peers out of its pram
The simile used here is the comparison of the peering, you can find it easily because of the use of "as". The significance here is that a baby is peering from its pram into a world it barely comprehends or understands - everything is new, exciting, but also scary.
we cling to our last pleasures as the tree clings to its last leaves
Here we have another simile, again identified by the use of "as". In this line, we are asked to consider a deciduous tree about to enter winter - the harshest of seasons. The last leaves seem to cling to the branches, withering and dying, rather than falling to the ground in golden autumn colour splendour.