Bugsy, if I'd discovered those messages on my dh's phone, I know it would niggle away at me so much, however many times tried to explain it away to myself. I would have to take things further in some way.
You can, of course, ask him outright, but as you say, and I agree with you, you don't want to hurl around accusations unless you are in a position of strength. Right now, he has the moral upper hand - he can accuse you of snooping on him.
But, I think you need to find out more to see if your fears are well founded.
FWIW, I think you need to surprise him, see what his reaction is when you catch him off guard. Suggest something totally unexpected. I know you have a baby and so that means you are less mobile and spontinaiety will be hard, but would any of the following suggestions work practically? ( remember you are not necessarily indending to carry them through, they just have to sound plausible)
How about suggesting you visit him for one of his work trips abroad? or say some good friends of yours will be in the same foreign area as him and how about meeting up with them after work? Or suggest holding a party for some of his colleagues? Or, when he is back in England, turn up by surprise at his work as he is leaving one evening with a restaurant booked for a meal? Or say that one of your friend's older children wants to get a work placement in a department like his - could he set the ball rolling? etc etc
Anything really that links his work life with you. And make the suggestion when you are face to face with him. If he seems really uneasy or evasive then you will be able to note it.
It must be so hard to detect any changes in your dh if he is not at home for long periods of time. I really feel for you here.
And as you say, if the text messages stopped in December it looks like whatever happenend or didn't happen could be at an end. And also, the woman who sent the messages might have had a crush on your dh, and he managed to extricate himself from a potentially awkward situation and that was that.
I do hope you get to the truth, and hope it doesn't take too long. That waiting feeling is not pleasant.