I've spent a long time looking into this with the Three 2nd line tech support guys.
Basically, it doesn't matter too much which carrier you are on, as people are having issues on multiple carriers. iOS 10 just doesn't work well on 4G. This exacerbates itself when you have "Voice and Data" set to 4G, as the phone doesn't receive incoming calls.
The 10.0.3 fix only resolves 4G connectivity issues for iPhone 7 and 7+ on the Verizon network in the US, although the 10.1 beta is apparently much better for UK carriers and does seem to fix it.
What it comes down to is that until there is a 10.0.4 or a 10.1, you are best off making sure 4G is set only for data, and you may need to turn off 4G altogether. The best way to describe this is a very poor implementation of the 4G in iOS 10 by Apple, probably as a result of the Intel Modem they've elected to introduce, this time around.
Three's comment on this was that they are working with Apple to get the issues resolved in a new iOS release.