Hi Liam,
I got your email and noticed that you posted here. Sorry for the late reply, but I've had a busy couple of days (telling everyone my girlfriend is pregnant

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We have a couple of players based in Carlisle (Steve and Mark Temple). These guys both play for our our British League 2nd team and are good players (Steve England top 200). They don't play in a league (as Carlisle does not have one), but practice together. If you want, I can put you in touch?
I'm not sure how old you are. If you're still young, the Whitehaven Harbour Youth Project have a table tennis session on a Wednesday night. A coach from Barrow (Duncan Crawford) has done some work up there in schools, I can find out which ones if you want?
Apart from that, your only choices are Barrow and Kendal. Millom do have a team in the Barrow league. That is a bit closer to you and they might have a practice session. Again, let me know and I can get a contact number for you.
Just for your information. The Barrow Table Tennis Centre (Furness Academy, West Avenue, Barrow-in-Furness, LA13 QQE) is open to the public between 7pm and 9pm Tuesday night. I also run a session 7pm to 9pm Monday night for the towns British League players (invite only - if you're good, you are more than welcome).
Hope this helps.
Barrow TTC.