An organisation whose IT I'm involved with has offices in a country which blocks access to various well know services such as Skype. I can get around the issue by routing all the traffic over IPSec to the HQ office but that has limited bandwidth.
Is there any way I could route all the traffic via an IPSec connection to a cloud provider and break out to the Internet there? I could either use a dedicated service for this purpose, if such a thing exists, or build a service using a generic cloud provider and a gateway product.
I have tried using Azure but this does not seem to be achievable.
Yup, ZScaler would fit your requirements nicely. they have a Security as as Software "SaaS" solution that you could use to route your traffic to them first, and then to the internet.
https://www.zscaler.com/
You can try this using a slightly modified Amazon Web Services VPC (Virtual Private Cloud).
First you need to create a VPC and a VPN connection to that VPC - Amazon supports a fair amount of hardware, including SonicWall, Juniper and Cisco units and provides "drop-in" configurations for most things.
You can then create a NAT instance to route traffic from your "private" VPC subnets out to the internet.
You can then route traffic to your NAT instance by changing your network's default gateway to the internal IP of your NAT instance, which is routable over your VPN.
Be aware though (and this does not in any way consitute legal advice) that circumventing access policies could be illegal - Amazon would likely be the first to roll over and play up to the authorities in the event of you being prosecuted.
Just adding on to @Noor's answer, this is the service you probably need.