Large list to dataframe with list identification in a new column

Question

Using the example data "hourly_time_series" from IETD package, I created a large list (each sublist are dataframes of different sizes) with IETD package. Each list represents a rainfall event.

library(IETD)
HU <- drawre(Time_series=hourly_time_series,IETD=5,Thres=0.5)
RE <- HU$Rainfall_Events

I need to convert RE to a dataframe with an additional column with the number of the rainfall event (as an ID) to separate them easily. I tried with bind_rows() and rbindlist() functions but these don´t preserve the rainfall ID. How Could I do this? The desired output as an example is:

event	Date	depth
1	2000-01-06 04:00:00	1.0
1	2000-01-06 05:00:00	0.0
1	2000-01-06 06:00:00	1.5
1	2000-01-06 07:00:00	1.5
2	2000-01-06 20:00:00	0.5
2	2000-01-06 21:00:00	0.5
.	. .	.
.	. .	.
.	. .	.

Hope you could help