FWIW I had an engine failure on rotation in a big twin at Heathrow a few years back. Gave a quick 'Mayday XXXXX engine failure' - not because we were in any immediate danger, but because it would alert Tower that we had a problem & he shouldn't expect us to to 'do the expected'. We then carried out all the necessary checks in blissful p&q, without being hassled for frequency changes etc etc.
ATC were fantastic (that'll be a 'no delay' next time I fly guys
) & all ended up happily ever after.
No regrets on the Mayday. I'd do the same tomorrow.