HR send flowers/gift card for big life events like marriages, births, bereavement, retirement.
Leavers - very much depends on how long you've been there. Usually there would be a card/small gift for a long term member of staff organised by their immediate team. The card might go around other teams to sign but no expectation to contribute. If you've been there a very long time your supervisor gives a leaving speech in the office recounting stories etc and says you'll be missed but this seems to be pretty rare these days.
Teams also organise a small gift for births, again might pass the card to neighbouring teams to sign. No obligation to contribute. This might be a highchair or a book, depending on the size of your team.
Birthdays this very much depends on the team within my company. Never did before my current director but she likes to do it for our team. Usually something small like a box of chocs, handcream, book alongside a card. We all chip in a couple of £. Personally I think a card for this would be fine.
For Xmas, we exchange small token gifts (chocolate usually). Other teams the head of buys everyone a bottle of fizz at Xmas and in other's they do an advent calendar 'secret santa', other teams do a traditional secret santa. The firm also give a gift card.
If someone was off Ill for a significant illness HR would send flowers as a get well soon gesture, your team might also send a card/chocs. I had an op and was off for 1m for example.
We also bring in cake for our own birthdays to share with our team.
We all bring a treat back from big holidays to share in our team meeting.
I think it's nice, but I can imagine with big teams £2 here and there really adds up.