The problems will come when they hit the first rills (drainage channels) that have been happily draining water away from where the coal faces were for the last 500 years, and nobody will know about them until the borings get flooded...
Perhaps we should dig up Marc Brunel - he had a few water breakthroughs on the Thames tunnel.
It wouldn't be without precedent, with the Severn Tunnel being at the extreme end of the examples in Britain. Work on the big long sewer from Hanham to Avonmouth encountered quite a few springs and underground waterways. A friend who plastered my walls in the house we bought in 1985 had worked on it, and was briefly famous in an anonymous sort of way when the tunnel he was digging broke through into a shaft outside the then HTV studios, and his was the hand that shook the hand of the waiting reporter. You don't get telly like that any more. A grout made of mainly power station fly ash, and costing ten times the price of normal grout, was used because it would go off under water if need be. They were not so deep in places - a hundred feet or more below Totterdown, but in Hill Avenue by Victoria Park, they started to find bricks dropping from the foundations of the houses above. Nobody above knew, and the houses were left left much stronger than when they were thrown up.
All of which beggars the question as to why tunneling should be such a problem or so expensive, if Wessex Water were able to drill something big enough to drive a Mini through with little disruption, and in a short timescale.