The most common and most likely answer to this crossword clue is the 8 letter word CO-HOSTS
I've seen this crossword clue in Independent
C
O
-
H
O
S
T
S
More clues leading to the result CO-HOSTS
Buddy explains!

The straight part
We know that "Hammond and May (the TV presenters, not the politicians!)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hammond and may (the tv presenters, not the politicians!) = co-hosts.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CO-HOSTS mean?
CO-HOSTS noun- A joint host alongside another (compare co-star).
- To act as a joint host.
- To store data on a shared server (as in web hosting).