That's a 38mm (= 3.8cm) pole then.
Looking at the models sold by Argos, you should ignore this one
https://www.argos.co.uk/product/8671637
because it can't accommodate poles more than 3.2cm in diameter.
Your pole would fit into this one but, because it can take a pole up to 4.5cm in diameter, you'd end up with a rather loose fit:
https://www.argos.co.uk/product/7428805
The same applies here:
https://www.argos.co.uk/product/3098363
This one though takes poles up to a maximum diameter of 3.8cm, so (assuming that you've measured accurately!), it should provide a nice snug fit:
https://www.argos.co.uk/product/4599737
This product, from B&Q, is cheaper though and also accepts poles up to 3.8cm in diameter:
https://www.diy.com/departments/tobago-black-parasol-base-15kg/1851206_BQ.prd
(It's also heavier, so it might provide greater stability)