You are not the first to compare the two, from Infected, Zombies And Triffids
The plants that take over the world in Day Of The Triffids have many
characteristics of zombies. In particular, they are slow-moving and
can be dealt with one on one (as long as you’re not blind that is), it
is when they appear en masse that they can over-run almost any human
defences. In this respect, you could replace then with zombies or
infected and the story told would remain pretty much the same. This
proposition is supported by the fact that this is what happened with
28 Days Later, which is almost scene for scene a homage to the
original Day Of The Triffids book but with rage victims replacing the
eponymous predatory plants.
Also from the The Day of the Triffids wiki page
According to director Danny Boyle, the opening hospital sequence of
The Day of the Triffids inspired Alex Garland to write the screenplay
for 28 Days Later
So yes, it's clear 28 days later was directly inspired by The Day of the Triffids