I suspect I'm missing the obvious here but, for the life of me, I can't see what!

We have Vigor 2820 (Firmware 3.3.7.6) and Vigor 2830 (Firmware 3.6.7)

Neither of these routers will allow a remote management over https. Http and Telnet are fine.

If I attempt to use IE11 I get this error (note the strange spelling):

This page canrsquo;t be displayed
Turn on TLS 1.0, TLS 1.1 and TLS 1.2 in Advanced settings and try connecting to https://xxx.xxx.xxx.xxx again. If this error persists, contact your site administrator.

Using Chrome 42.0.2311.152m I get this error:

This web page is not available

ERR_SSL_VERSION_OR_CIPHER_MISMATCH
Hide details
A secure connection cannot be established because this site uses an unsupported protocol.

Could any kind soul give me any pointers.

Many thanks.

try at System Maintenance >> Management > internet access control > Allow management from the Internet and tick the ones you need
That should allow to access remotely

You are getting this problem because only SSL 3.0 is supported - at least on the 2820 - and the browser developers have been switching this off after the POODLE vulnerability was discovered.

http://www.pcworld.com/article/2842155/google-to-kill-off-ssl-30-in-chrome-40.html

http://windowsitpro.com/patch-tuesday/patch-tuesday-3038314-disables-ssl-30-only-ie11

https://blog.mozilla.org/security/2014/10/14/the-poodle-attack-and-the-end-of-ssl-3-0/

In Internet Explorer you can turn on SSL 3.0 again by going into Internet Options > Advanced tab > Under the Security group select "Use SSL 3.0". This is at your own risk though.

Many thanks guys for your input.

Changing the security settings in IE didn't help. Instead I've created a VPN and used the local LAN IP address.