I'm trying to get PHPMailer on my web server (VPS) to talk to my remote mail server. I get the response:

Connection failed.
Error #2: stream_socket_client(): unable to connect to mail.bristolweb.net:587
(Connection timed out)

I've tried this with port 25 and 587 (with appropriate changes) but it always gives the impression the call never gets outside the parent server. Incoming to 80 and 443 work fine. Ping to google works (but not to my mail server as it's not allowed). Mail server works well and has been for years. Telnet fails (but possibly would anyway - can't remember what I blocked on mail server).

I THINK it's a blocked port but can't work out how. I've been searching for a couple of days but all the likely hits return something like "Talk to your hosting service" or "it's firewall.

My iptables at present is short:

*filter
# Allows all loopback (lo0) traffic and drop all traffic to 127/8 that doesn't use lo0
-A INPUT -i lo -j ACCEPT
-A INPUT ! -i lo -d 127.0.0.0/8 -j REJECT
# Accepts all established inbound connections
-A INPUT -m state --state ESTABLISHED,RELATED -j ACCEPT
# Allows all outbound traffic
-A OUTPUT -j ACCEPT
# Allows HTTP and HTTPS connections from anywhere (the normal ports for websites)
-A INPUT -p tcp --dport 80 -j ACCEPT
-A INPUT -p tcp --dport 443 -j ACCEPT
# Allows SSH connections
-A INPUT -p tcp -m state --state NEW --dport 22 -j ACCEPT
# Allow ping
# note that blocking other types of icmp packets is considered a bad idea by some
# remove -m icmp --icmp-type 8 from this line to allow all kinds of icmp:
-A INPUT -p icmp -m icmp --icmp-type 8 -j ACCEPT
# log iptables denied calls (access via 'dmesg' command)
-A INPUT -m limit --limit 5/min -j LOG --log-prefix "iptables denied: " --log-level 7
# Reject all other inbound - default deny unless explicitly allowed policy:
-A INPUT -j REJECT
-A FORWARD -j REJECT
COMMIT

I've added 25 and 587 as inputs and outputs but, as expected, no difference.

At one point I installed DMA (Dragonfly) smtp MTA but that couldn't connect either.

Usually I can find the answer to problems online but this has me beat. :(