I can't find anything official to suggest there's any difference between using 112 and 999. Historically, 999 is used in the UK. Outside the UK, 112 had wider use and so its use was adopted onto the UK systems, with calls routed to the same emergecy operations as 999.
There's also nothing to suggest that any ability to locate your mobile using triangulation (based on nearby transmitter masts) is lost if you use 999 rather than 112. I wouldn't suggest anyone relying on the emergency services being able to find you quickly from such information in any case.
If you're working in the woods (as I guess is the main interest here), make sure you have your location details ready to give. If your position is away from a main road and working alone, you might be prepared enough to leave a notice at the main road advising the paramedics where to find you.
This site http://www.emergencysms.org.uk/ appears to be the official site of the body that runs the service that allows you to send texts to 999. It does reiterate the need to register first as stated in the video.
I've just sent "register" to 999, received my first response, then sent "yes" to 999 and received an acknowledgement that I'm registered. The texts refer to http://www.emergencysms.org.uk/ for further details. I then sent "register" to 112 and received a reply stating I'm already registered. So for texting purposes too, either 112 or 112 are handled.
I understand that the UK mobile networks no longer permit emergency calls from handsets that don't have a SIM due to the large number of false/hoax calls that couldn't be traced. So you do need a mobile with a SIM. It will use any network it can find if you're out of range of your own network provider.
There's also no evidence to support the myth that in the case of an emergency, a phone with a dead battery will still be able to make an emergency call