This report from Public Health England says that Delta now makes up 97% of the genotyped cases.
This report from Public Health England says that there have been a few cases of Lambda from international travel, but it does not seem to be out-competing Delta and does not seem to be particularly vax-evasive. It sounds like there’s nothing deeply concerning with Lambda.
This preprint says that the initial viral load from Delta is 1000x that of earlier strains, which could explain why it is so much more contagious.
This article has a great diagram summarizing different studies of vaccines against different strains: