I was unaware it could solidify. Can you stick a nail in the end of the syringe to open it up and make the syringe work that way?
I see that S&S is out of stock.
https://www.sjscycles.co.uk/lubricants/finish-line-extreme-fluoro-ss-coupling-approved-grease-20g-syringe/I would expect that any bike company in UK that sells a frame with S&S couplers would know where you could buy it. Or, was SJS the only one in UK that sold an S&S bike?
I would use something else until you can find the right stuff later. But you might not want to tighten your couplers toooooo tight if you use a lower grade of grease. A few years ago one of my couplers came a bit loose during a ride, I now always carry a wrench that can tighten the couplers. An old style bottom bracket wrench might also work.
I put sleeves cut from an old inner tube over each end of my S&S coupler nuts to keep the dirt out of the threads. I think the key is to keep the threads clean. See photos.