Problem with ERR_SSL_VERSION_OR_CIPHER_MISMATCH occurring and issue with updating Skype (not sure if two problems or one!)

Question

I have two problems which may or may not be connected and I need some help in knowing where to look.

Firstly, I can't update Skype - the updater fails to connect to the Skype repository and cannot download the update.

Trying to update from the terminal by running:

sudo apt-get update 

gives this error:

Ign:28 https://repo.skype.com/deb stable/main DEP-11 64x64 Icons
Err:30 https://repo.skype.com/deb stable/main amd64 Packages
  gnutls_handshake() failed: Handshake failed
Fetched 7,442 B in 5s (1,476 B/s)
Reading package lists... Done
W: The repository 'https://repo.skype.com/deb stable Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: Failed to fetch https://repo.skype.com/deb/dists/stable/main/binary-amd64/Packages  gnutls_handshake() failed: Handshake failed
E: Some index files failed to download. They have been ignored, or old ones used instead.

Secondly (and the reason I think it may be related perhaps), I can't access some webpages, including https://www.skype.com, because it throws up:

ERR_SSL_VERSION_OR_CIPHER_MISMATCH (or SSL_ERROR_NO_CYPHER_OVERLAP in Firefox).

I am running Ubuntu 16.04 LTS and using Chromium. I connect to the internet via WiFi.

I have tried running Chromium with a fresh new profile and the error persists.

I have tried Firefox but I get:

(SSL_ERROR_NO_CYPHER_OVERLAP)

If I run Chromium from a terminal I get errors such as:

[30008:30040:0924/195356.390049:ERROR:ssl_client_socket_impl.cc(943)] handshake failed; returned -1, SSL error code 1, net_error -113

I have tried running:

 sudo apt-get --reinstall install ca-certificates`