Around me, the most popular boys names (for years) have been Archie, Oscar and Teddy. I also know quite a few boys called Oliver, Noah, Lucas, Leo, Jacob and Thomas, although most of these are 8+ now so not really young children. Arlo, Jude, Reuben, Roman and Hudson seem very up and coming in the under 5s around me. David is super popular at my school, although I feel this is quite an anomaly when you look at national stats (we're in a very multicultural area and most of them are of African or Eastern European heritage).
For girls, Isla, Olivia and Sophia/Sofia have been popular for years. I know lots of girls called Sienna, Evie and Maya, although again these tend to be older girls now so not as many young ones. In the under 5s, it's all about Ivy, Harper, Mila and Aria right now. Poppy, Phoebe and Mabel are cropping up more too.
Anomalies in terms of names which are popular in the national stats, but seemingly not around me at this point in time:-
Theo/Theodore, George, Henry, Ava, Amelia, Lily, Isabella/Isabelle, Florence, Margot and Maeve.