If I wanted to try contact lenses, could I just order some on Amazon, using the dioptric values of my current glasses?

None of the ones on Amazon are prescription that I’m aware of.
Did you find some that asked for your vision prescription?

I found that they all have different diametres and “base curves”, and the little info card from the optometrist that I got my glasses from, only lists the dioptric values for each eye, which I do not even know if they are 1:1 applicable to contact lenses.

Specsavers over here will take an online order if you have an up to date prescription. The stores are also open for business.

This is what they say on their website: “Having a valid contact lens specification when ordering contact lenses is essential. This is to make sure that you order the lenses that are right for your eyes. Ordinarily, we would verify the specification with your optician to make sure you get the right product. However, given the current coronavirus situation, we recognise that for a time it may be difficult to verify specifications with your optician. Where this process cannot be completed, we will apply our professional judgment when considering to maintain your supply of new contact lenses and refreshing them at the frequency recommended by your optician.”

1800contacts gives you an online eye test, if that helps.

I don’t think that would work in most cases. Too many variables. If it’s just online services you’re looking for (not specifically Amazon), MisterSpex is easy to use. They have an online eyesight evaluation, but it’ll only be available if you’re under 40, not diabetic, human, and just moderately sight-impaired.

If your optician happens to be one of their partners, you won’t even need the test.

Eyeball person

The lens needs to be fitted to the shape and size of your eye.

As well the dioptric value a contact lens prescription also includes the diameter of the lens and the base curve of the eyeball. These are usually more of an issue with hard lenses, soft lenses are bit more forgiving so you might be able to get away with by going with the most common size of both if you are trying daily disposable lenses.
Having said that if you’ve never worn contacts before the session after the eye exam where someone teaches you to put them in and take them out without blinding yourself is probably worth the price of admission alone. Also most opticians will throw in some free trial lenses (in a marketing strategy not too dissimilar to the dealer who hangs around playgrounds).