Never done any beach fossicking, but what you're looking for is Topaz, aka Killiekrankie Diamonds, clear or possibly lightly coloured, hard Moh 8 so will scratch a lot of other stones but can only be scratched by harder stones like Sapphire, cold to the lips, and a soapy feel. Spectacular sparkle when cut. The are often 8 sided in cross section (orthorhombic). Specific gravity of approx 3.5 so they tend to sink in waterways. You'll probably find most are water worn and rounded.
Probably worth getting a series of graded sieves so you can get rid of the rubbish and tiddlers first and stick to the bigger stones so you can get them cut.
Have fun, you may find other interesting things as well.
The story behind their name is as brilliant as the stones themselves:
https://www.examiner.com.au/story/7020005/gems-bedazzled-londons-legal-eagles/