I achieve something similar using an IKEv2 site-to-site IPsec VPN between a Raspberry Pi 3 at home and a VPS in a different country. In my case, however, I live in the UK and my requirement is to have traffic from certain devices on my LAN to automatically go over the VPN and egress from a different country.
It's a bit complicated and fiddly to set up, and it took me a while to get to grips with IPsec, but it works a treat.
I have a /24 network at home and a smaller subset of it (a /28) is included in the "encryption domain" of the VPN and gets automatically routed over the VPN if devices with those IPs use the Raspberry Pi as their default gateway. Simple as that.
To achieve that, I set up static reservations for those devices on my DHCP server (in the EdgeRouter):
static-mapping PS3 {
ip-address 192.168.1.33
mac-address fc:0f:e6:cf:57:8d
static-mapping-parameters "option routers 192.168.1.7;"
}
As you can see, that reservation get a different default gateway, 192.168.1.7 (IP address of the RPi), instead of 192.168.1.1, which is my EdgeRouter, which is the default gateway for all other devices at home.
The subnet for the encryption domain is 192.168.1.32/28 (192.168.1.33 - 192.168.1.46 usable). I used the
auto=route option in ipsec.conf which installs kernel traps that automatically bring the VPN up when it detects traffic between the left and right subnets (in case the SA is not up).
In your case, all you need is a VPS in the UK (around $5 a month) and a £30 Raspberry Pi (or any capable router or Linux machine). I tried various commercial VPN providers, even the really big ones, and their IP addresses were always easily detected by various content providers as a VPN exit point. Some people have reported better success by purchasing a dedicated static IP from VPN providers, which tends to be outside of their usual VPN pools, but YMMV.
If you need more details, let me know