The two pronunciations heard in the podcasts there are two entirely different phenomena. The second, the pronunciation of "graind", is part of the presenter's regional accent.
The first, however, is not. It is a very good example of alveolar assimilation. The sound /s/ is made with the rims (sides) of the tongue on a little shelf behind your teeth called the alveolar ridge. Sounds made on or near the alveolar ridge in English are very unstable. They change a lot when we speak depending on the different sounds they are next to. This happens most often when they are at the end of a word or syllable.
When a word final /s/ happens before the sounds /ʃ/ or /ʒ/ (the sound at the beginning of shower and genre), then in normal speech it will nearly always change to /ʃ/.
- this shoe ---> /ðɪʃ ʃu:/ [pronounced "thish shoe"]
- this genre ---> /ðɪʃ ʒɒnrə/ [pronounced "thish genre"]
When /s/ occurs before some other sounds ...
- /r, j, tʃ, dʒ/ the sounds at the beginning of right,
yoyo, church and judge
... it will sometimes change to /ʃ/. It won't happen all the time, but it happens quite often. So you will occasionally hear:
- thish rubbish
- thish year
- thish church
- thish jumper
This happens in most accents of English, including RP. So the presenter here is giving you a very good example of alveolar assimilation! If you are interested in what happens to different sounds in real speech, have a look here. These are lecture notes from John Wells, published on the UCL university website.