SIM800L connects to O2 but not Three

I have my SIM800L running on 4V from a 2A-capable supply and connected to a 5V Arduino through a bidirectional level shifter.

If I put my Giffgaff SIM card from my iPhone in it, it connects. (Giffgaff runs on the O2 network. The LED flashes once per second for around 4 secs then reverts to once per 3 secs.)

But I want to use it with a free data SIM I get from Three. I registered this in a Three mobile data dongle and in that, it connects to the Internet and receives texts. (You have to top it up to send texts.) In the SIM800L it just flashes once a second for ever.
I get:
+CREG: 0,0


Is there a compatibility problem between the SIM800L and the Three network?

Does the three network support 2G?
SIM800L is 2G only module

Thank you for your reply. I believe it does support 2G but I’m having difficulty finding a positive statement to that effect, though since 2G is needed for older feature phones I’d be very surprised if not.

In fact I think my problem is with the power supply (ICL7663 + external NPN bypass transistor). A test yesterday suggested it wasn’t able to deliver as much current as I designed it to. I’m awaiting delivery of a MIC29302 low dropout regulator which should do better, and will report back when I’ve had a chance to try it.

I now have it supplied at 4V through a MIC29302 low dropout linear regulator. With a 2 ohm resistor across the output the voltage only drops by 0.06V.

But the results are exactly as before - Giffgaff SIM works, but Three SIM fails to connect to the network.

In fact I’ve now established that the Three UK network doesn’t support 2G. It did so previously only through agreements with other suppliers but evidently they decided it was a market segment they could afford to walk away from.

I now have to make a choice: (a) a much more expensive 3G module, (b) a bargain basement PayG SIM, (c ) use a USB mobile dongle with the free Three SIM and a Pi rather than Arduino. But my original objective of a very simple and cheap SMS to TV IR code gateway for a dementia sufferer with no ongoing fees seems out of reach.

Use SIM5320 for 3G. Why not use the O2 sim if it works?

SIM800L: £3; Three SIM: Free
SIM5320: £47; O2 SIM: £5/month

This started as a pocket money project but is probably no longer viable.

My client uses SIM800C in UK. Let me check which network he uses.