"cheerio" means goodbye. What does "all that rot" mean?
"...things/stuff [with a hint of depreciation] like that". The two idioms put together sound a bit dated - maybe early twentieth century (it sounds to me a bit like Enid Blyton - who wrote for many years but is probably most famous for her "Famous Five" books in the 1940s and '50s); the speaker is suggesting that the idea of formal leave-taking [=saying 'goodbye'] is perhaps inappropriate - perhaps a schoolboy saying goodbye to a friend who he's not going to see for a while [in that series, it might be Dick saying goodbye to George at the end of the summer holidays].
Excuse all the hypothetical contextual stuff - "all that rot"!