Paul - limestone/chalk tends to produce decent water atthough it can be difficult to get at. If there is an old well its fair to assume there is water there. There may be old records on
http://mapapps2.bgs.ac.uk/geoindex/home.html?theme=boreholes (you need to select the borehole and water wells data sets). If not for your site then a site close by will give you an idea of the geology. If you get the water tested I'd empty the well a couple of times, letting it recharge before testing, your local Env Health Dept should do it and importantly should be able to give an interpretation of the results.
Good luck
