The line falls from Badminton station site at 1:300 in an increasingly deep cutting in porous limestone to the tunnel. There's a watercourse on the surface that runs intermittently (and is carried across the cutting in an aqueduct) and the surface area of the cutting itself will catch a considerable amount of rain, and attract more should the water table rise sufficiently.
There are records of a series of boreholes from 2003 as the railway investigated the geology. The records are confidential but the locations can be viewed here:
https://mapapps2.bgs.ac.uk/geoindex/home.html?layer=BGSBoreholesNow, that site doesn't allow a link to a location, but just search for 'Badminton' and work from there.
You'll also find brief notes on the construction shafts for the tunnel - the whole lot are on the following link, just two pages with brief handwritten notes for each, and a sketch of a lengthwise slice of the ground. These aren't from the time the tunnel was built - it looks as though someone was out on a fact finding mission - there is possibly a date 27/8/49 towards the foot of the first page.
On the second page, the words 'From 1 to 2, 10 hours for water to travel' is expressive of
something.
https://api.bgs.ac.uk/sobi-scans/v1/borehole/scans/items/394592Various farms thereabouts have boreholes with healthy amounts of water, so it looks to be the usual Cotswold story, plenty of water around until you need some, at which point you can't find any - but if there's something that needs to stay dry, it experiences an irregular drenching as the water table rises.
The engineer for the Thames and Severn canal found this - surveying in February and moving through a country, in a wet February, criss crossed by little rills and with water bursting out of the ground all over the shop he was sanguine about the water supply. Once the canal was open and at the height of a cotswold summer drought with even the trees looking thirsty and water slurping out of the channel through holes in the puddle made by winter springs but now dropping the water into voids beneath the ground locally known as 'Lizens'... this did not make for a happy experience all round.
For anyone itching to read a more complete borehole record, this one's south of the motorway and some way from the line, but probably close enough to indicate why there's a lot of water in the ground thereabouts.
Reference: ST87NW42
Name: NETTLETON 2
Water Well Reference: N/A
Precision: ± 10 METRES
Length (m): 110.03
Date: 1936
Easting: 382670
Northing: 179460
Scan Quality: not Entered
https://api.bgs.ac.uk/sobi-scans/v1/borehole/scans/items/396302Mark