Access to internet from containers connected to bridge - docker

Question

I’m now cracking my nuts trying to get containers connected to custom bridge network reach to internet.
Small background, I have internet facing server running the Docker daemon. As all my applications are web applications I need to have single point for maintaining SSL certificates and access rights to them.
As a solution I deployed Nginx reverse proxy (nginx-proxy-manager) that is handling all incoming traffic, serving the SSL certificates and deployed all web containers into the same custom network bridge.
It turned out, that in this way applications can communicate each other (so the reverse proxy can pass the traffic to them which is what I wanted), but they are unable to reach out the internet.
Is there any possible way how to with this setup allow containers speak to internet?
Many thanks for eventual hints.
lsb_release -a
No LSB modules are available.
Distributor ID: Debian
Description: Debian GNU/Linux 10 (buster)
Release: 10
Codename: buster
docker version
Client: Docker Engine - Community
Version: 20.10.22
API version: 1.41
Go version: go1.18.9
Git commit: 3a2c30b
Built: Thu Dec 15 22:28:20 2022
OS/Arch: linux/amd64
Context: default
Experimental: true
Server: Docker Engine - Community
Engine:
Version: 20.10.22
API version: 1.41 (minimum version 1.12)
Go version: go1.18.9
Git commit: 42c8b31
Built: Thu Dec 15 22:26:12 2022
OS/Arch: linux/amd64
Experimental: false
containerd:
Version: 1.6.15
GitCommit: 5b842e528e99d4d4c1686467debf2bd4b88ecd86
runc:
Version: 1.1.4
GitCommit: v1.1.4-0-g5fd4c4d
docker-init:
Version: 0.19.0
GitCommit: de40ad0
docker network ls
NETWORK ID NAME DRIVER SCOPE
d95bb7471827 bridge bridge local
2f660f266735 host host local
36c3efe85b83 none null local
d9eaf06a2693 reverseproxy-nw bridge local
# docker network inspect d9eaf06a2693
[
{
"Name": "reverseproxy-nw",
"Id": "d9eaf06a26936b155fac6568980d5f8fd685531bdc797911592e112a3b70a8a3",
"Created": "2022-08-15T20:26:29.046077109+02:00",
"Scope": "local",
"Driver": "bridge",
"EnableIPv6": false,
"IPAM": {
"Driver": "default",
"Options": {},
"Config": [
{
"Subnet": "172.18.0.0/16",
"Gateway": "172.18.0.1"
}
]
},
"Internal": false,
"Attachable": true,
"Ingress": false,
"ConfigFrom": {
"Network": ""
},
"ConfigOnly": false,
Switching to the host network works, so it looks that this problem is related to the bridge network.